A characterization of pseudo-Einstein real hypersurfaces of a complex space form

• Autorzy: Kon M

Identyfikatory

DOI

10.1515/JAA-2013-010

• Języki publikacji: EN

Abstrakty

EN

We give a characterization of pseudo-Einstein real hypersurfaces of a complex space form. We prove that if the Ricci tensor S of a real hypersurface M of a complex space form with constant principal curvatures satisfies S(X, Y)=ag(X, Y) for any X, Y ∈ T ₀(x), where a is a function and T0 is the holomorphic distribution on M, then M is a pseudo-Einstein real hypersurface.

Słowa kluczowe

EN

real hypersurfaces; Ricci tensor; pseudo-Einstein real hypersurface; holomorphic distribution; constant principal curvatures

PL

hiperpowierzchnia rzeczywista; tensor Ricciego; rozkład holomorficzny; krzywizna stała

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2013
• Tom: Vol. 19, nr 2
• Strony: 167--179
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kon M

• Faculty of Education, Shinshu University, 6-Ro, Nishinagano, Nagano City 380-8544, Japan

Bibliografia

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• [3] M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), 137-149.
• [4] M. Kimura, Sectional curvatures of holomorphic planes on a real hypersurface in PΠ(c), Math. Ann. 276 (1987), 487-497.
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• [6] S. Montiel, Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37(1985), 515-535.
• [7] M. Ortega, Classifications of real hypersurfaces in complex space forms by means of curvature conditions, Bull. Belg. Math. Soc. 9 (2002), 351-360.
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• [9] Y. Tashiro and S. Tachibana, On Fubinian and C-Fubinian manifolds, Kodai Math. Sem. Rep. 15 (1963), 176-183.
• [10] K. Yano and M. Kon, CR-Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhauser, Boston, 1983.