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Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres
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We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.
Abstract
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.
참고문헌 (7)
- E. Calabi, "Construction and properties of some 6-dimensional almost complex manifold", Trans. Amer. Math. Soc, 87, pp.407~438 (1958)
- A. Gray, "Curvature identities for Hermitian and almost Hermitian manifolds", Tˆohoku Math. J, 28(4), pp.601~612 (1976)
- H. Hashimoto, "Extrinsic homogeneous almost Hermitian 6-dimensional submanifolds in the Octonions", Kodai Math. J, 30(3), pp.297~321 (2007)
- C. Lebrun, "Orthogonal complex structures on S6", Proc. Amer. Math. Soc, 101(1), pp.136~138 (1987)
- A. Newlander, "Complex analytic coordinates in almost complex mani- folds", Ann. of Math, 65, pp.391~404 (1957)
- K. Sekigawa, "Almost Hermitian manifolds with vanishing first Chern class or Chern numbers", Rend. Sem. Mat. Univ. Politec. Torino, 50(2), pp.195~208 (1992)
- W. A. Sutherland, "A note on almost complex and weakly complex structures", J. London Math. Soc, 40, pp.705~712 (1965)
관련 논문AI추천
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