Books for Complex Differential Geometry: index approach
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What are some books (if any) that tackle complex differential geometry with tensors in index notation?
My studies have led me to an area where I think I must proceed with that field; however, I have only encountered (real) differential geometry with tensor index notation and as such would have to do significantly more reading if the canon extending the notions to complex manifolds does not have a similar approach. I have scanned through some books such as Huybrechts and Demailly: They seem comprehensible, but I have trouble seeing how their formulation may apply like real tensors to relativity: Alternatively what books can give me the background/prerequisites to understand the physics applications of the language used in those books?
differential-geometry reference-request complex-geometry
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
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add a comment |
$begingroup$
What are some books (if any) that tackle complex differential geometry with tensors in index notation?
My studies have led me to an area where I think I must proceed with that field; however, I have only encountered (real) differential geometry with tensor index notation and as such would have to do significantly more reading if the canon extending the notions to complex manifolds does not have a similar approach. I have scanned through some books such as Huybrechts and Demailly: They seem comprehensible, but I have trouble seeing how their formulation may apply like real tensors to relativity: Alternatively what books can give me the background/prerequisites to understand the physics applications of the language used in those books?
differential-geometry reference-request complex-geometry
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
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1
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If you want something full of gory detail index calculations, you might try an appendix of a supersymmetry introduction. There they need a lot of complex and Kahler geometry so you might see an introduction included for the typical theoretical physicist even if you don't need any supersymmetry. If I find a specific, will turn into an answer.
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– AHusain
Jan 7 at 22:30
$begingroup$
@AHusain supersymmetry in what context? I just tried looking for some intros and, at least superficially, the ones I saw did not refer to geometry at all.
$endgroup$
– Quantumness
Jan 7 at 22:42
$begingroup$
Search for both Kahler potential and supersymmetry. The idea is quantizing maps from the spacetime into some Kahler manifold.
$endgroup$
– AHusain
Jan 8 at 4:06
add a comment |
$begingroup$
What are some books (if any) that tackle complex differential geometry with tensors in index notation?
My studies have led me to an area where I think I must proceed with that field; however, I have only encountered (real) differential geometry with tensor index notation and as such would have to do significantly more reading if the canon extending the notions to complex manifolds does not have a similar approach. I have scanned through some books such as Huybrechts and Demailly: They seem comprehensible, but I have trouble seeing how their formulation may apply like real tensors to relativity: Alternatively what books can give me the background/prerequisites to understand the physics applications of the language used in those books?
differential-geometry reference-request complex-geometry
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
$endgroup$
What are some books (if any) that tackle complex differential geometry with tensors in index notation?
My studies have led me to an area where I think I must proceed with that field; however, I have only encountered (real) differential geometry with tensor index notation and as such would have to do significantly more reading if the canon extending the notions to complex manifolds does not have a similar approach. I have scanned through some books such as Huybrechts and Demailly: They seem comprehensible, but I have trouble seeing how their formulation may apply like real tensors to relativity: Alternatively what books can give me the background/prerequisites to understand the physics applications of the language used in those books?
differential-geometry reference-request complex-geometry
differential-geometry reference-request complex-geometry
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
asked Jan 7 at 22:11
QuantumnessQuantumness
1243
1243
1
$begingroup$
If you want something full of gory detail index calculations, you might try an appendix of a supersymmetry introduction. There they need a lot of complex and Kahler geometry so you might see an introduction included for the typical theoretical physicist even if you don't need any supersymmetry. If I find a specific, will turn into an answer.
$endgroup$
– AHusain
Jan 7 at 22:30
$begingroup$
@AHusain supersymmetry in what context? I just tried looking for some intros and, at least superficially, the ones I saw did not refer to geometry at all.
$endgroup$
– Quantumness
Jan 7 at 22:42
$begingroup$
Search for both Kahler potential and supersymmetry. The idea is quantizing maps from the spacetime into some Kahler manifold.
$endgroup$
– AHusain
Jan 8 at 4:06
add a comment |
1
$begingroup$
If you want something full of gory detail index calculations, you might try an appendix of a supersymmetry introduction. There they need a lot of complex and Kahler geometry so you might see an introduction included for the typical theoretical physicist even if you don't need any supersymmetry. If I find a specific, will turn into an answer.
$endgroup$
– AHusain
Jan 7 at 22:30
$begingroup$
@AHusain supersymmetry in what context? I just tried looking for some intros and, at least superficially, the ones I saw did not refer to geometry at all.
$endgroup$
– Quantumness
Jan 7 at 22:42
$begingroup$
Search for both Kahler potential and supersymmetry. The idea is quantizing maps from the spacetime into some Kahler manifold.
$endgroup$
– AHusain
Jan 8 at 4:06
1
1
$begingroup$
If you want something full of gory detail index calculations, you might try an appendix of a supersymmetry introduction. There they need a lot of complex and Kahler geometry so you might see an introduction included for the typical theoretical physicist even if you don't need any supersymmetry. If I find a specific, will turn into an answer.
$endgroup$
– AHusain
Jan 7 at 22:30
$begingroup$
If you want something full of gory detail index calculations, you might try an appendix of a supersymmetry introduction. There they need a lot of complex and Kahler geometry so you might see an introduction included for the typical theoretical physicist even if you don't need any supersymmetry. If I find a specific, will turn into an answer.
$endgroup$
– AHusain
Jan 7 at 22:30
$begingroup$
@AHusain supersymmetry in what context? I just tried looking for some intros and, at least superficially, the ones I saw did not refer to geometry at all.
$endgroup$
– Quantumness
Jan 7 at 22:42
$begingroup$
@AHusain supersymmetry in what context? I just tried looking for some intros and, at least superficially, the ones I saw did not refer to geometry at all.
$endgroup$
– Quantumness
Jan 7 at 22:42
$begingroup$
Search for both Kahler potential and supersymmetry. The idea is quantizing maps from the spacetime into some Kahler manifold.
$endgroup$
– AHusain
Jan 8 at 4:06
$begingroup$
Search for both Kahler potential and supersymmetry. The idea is quantizing maps from the spacetime into some Kahler manifold.
$endgroup$
– AHusain
Jan 8 at 4:06
add a comment |
1 Answer
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One option:
Some searching led me to this set of lecture notes. On cursory reading it seems alright in its explanations and particularly useful in combining index notation with the coordinate-free approach; however, I am not sure how to evaluate it as it appears unmotivated and does not seem to tackle coordinate transformations (which to my understanding is what defines tensors). Further, it seems unclear how the concepts may be used outside of it simply existing.
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
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$begingroup$
One option:
Some searching led me to this set of lecture notes. On cursory reading it seems alright in its explanations and particularly useful in combining index notation with the coordinate-free approach; however, I am not sure how to evaluate it as it appears unmotivated and does not seem to tackle coordinate transformations (which to my understanding is what defines tensors). Further, it seems unclear how the concepts may be used outside of it simply existing.
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
$endgroup$
add a comment |
$begingroup$
One option:
Some searching led me to this set of lecture notes. On cursory reading it seems alright in its explanations and particularly useful in combining index notation with the coordinate-free approach; however, I am not sure how to evaluate it as it appears unmotivated and does not seem to tackle coordinate transformations (which to my understanding is what defines tensors). Further, it seems unclear how the concepts may be used outside of it simply existing.
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
$endgroup$
add a comment |
$begingroup$
One option:
Some searching led me to this set of lecture notes. On cursory reading it seems alright in its explanations and particularly useful in combining index notation with the coordinate-free approach; however, I am not sure how to evaluate it as it appears unmotivated and does not seem to tackle coordinate transformations (which to my understanding is what defines tensors). Further, it seems unclear how the concepts may be used outside of it simply existing.
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
$endgroup$
One option:
Some searching led me to this set of lecture notes. On cursory reading it seems alright in its explanations and particularly useful in combining index notation with the coordinate-free approach; however, I am not sure how to evaluate it as it appears unmotivated and does not seem to tackle coordinate transformations (which to my understanding is what defines tensors). Further, it seems unclear how the concepts may be used outside of it simply existing.
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
answered Jan 9 at 22:23
QuantumnessQuantumness
1243
1243
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If you want something full of gory detail index calculations, you might try an appendix of a supersymmetry introduction. There they need a lot of complex and Kahler geometry so you might see an introduction included for the typical theoretical physicist even if you don't need any supersymmetry. If I find a specific, will turn into an answer.
$endgroup$
– AHusain
Jan 7 at 22:30
$begingroup$
@AHusain supersymmetry in what context? I just tried looking for some intros and, at least superficially, the ones I saw did not refer to geometry at all.
$endgroup$
– Quantumness
Jan 7 at 22:42
$begingroup$
Search for both Kahler potential and supersymmetry. The idea is quantizing maps from the spacetime into some Kahler manifold.
$endgroup$
– AHusain
Jan 8 at 4:06