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June 2014 Twistor holomorphic affine surfaces and projective invariants
Kazuyuki Hasegawa
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SUT J. Math. 50(2): 325-341 (June 2014). DOI: 10.55937/sut/1424794189

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 holomorphic 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.

Citation

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Kazuyuki Hasegawa. "Twistor holomorphic affine surfaces and projective invariants." SUT J. Math. 50 (2) 325 - 341, June 2014. https://doi.org/10.55937/sut/1424794189

Information

Received: 20 June 2014; Revised: 25 September 2014; Published: June 2014
First available in Project Euclid: 11 June 2022

Digital Object Identifier: 10.55937/sut/1424794189

Subjects:
Primary: 53A15 , 53C28

Keywords: Affine immersion , twistor lift , twistor space

Rights: Copyright © 2014 Tokyo University of Science

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Vol.50 • No. 2 • June 2014
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