Pseudo-Bochner-flat locally conformal Kähler submanifolds

• Autorzy: Koji Matsuo
• Języki publikacji: EN

Abstrakty

EN

Let M̃ be an (m+r)-dimensional locally conformal Kähler (l.c.K.) manifold and let M be an m-dimensional l.c.K. submanifold of M̃ (i.e., a complex submanifold with the induced l.c.K. structure). Assume that both M̃ and M are pseudo-Bochner-flat. We prove that if r < m, then M is totally geodesic (in the Hermitian sense) in M̃. This is the l.c.K. version of Iwatani's result for Bochner-flat Kähler submanifolds.

Kategorie tematyczne

• 53C55: Hermitian and K\"ahlerian manifolds
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 2
• Strony: 305-315

Daty

wydano

2007

Twórcy

autor

Koji Matsuo

• Department of Mathematics, Ichinoseki National College of Technology, Ichinoseki 021-8511, Japan

Identyfikatory

DOI

10.4064/cm108-2-12