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Abstract
We study affine immersions with twistor lifts. Using a decomposition of a connection, we obtain several projective invariants for such affine immersions. In particular, affine immersions with holomorphic twistor lifts are considered. We can show the property that an affine immersion has holomor-phic twistor lifts is invariant under projective transformations and characterize immersions with holomorphic twistor lifts by vanishing of some of projective invariants. In the case of compact affine surfaces with holomorphic twistor lifts, we see a quantization phenomenon for one of the projective invariants which we obtain. Moreover, we prove that a real analytic twistor holomorphic affine surface with the symmetric Ricci tensor with respect to both complex structures is totally geodesic or totally umbilic. © 2014 Tokyo University of Science. All Rights Reserved.
Journal
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- SUT Journal of Mathematics
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SUT Journal of Mathematics 50 (2), 325-341, 2014
Tokyo University of Science
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Keywords
Details 詳細情報について
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- CRID
- 1390853649740911360
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- NII Article ID
- 120005649583
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- NII Book ID
- AA1075431X
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- NDL BIB ID
- 028765657
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- ISSN
- 09165746
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- NDL
- CiNii Articles