Displaying similar documents to “An Extension of Calabi's Rigidity theorem to complex submanifolds of indefinite complex space forms.”

Ideal CR submanifolds in non-flat complex space forms

Toru Sasahara (2014)

Czechoslovak Mathematical Journal

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An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.

An improved Chen-Ricci inequality for special slant submanifolds in Kenmotsu space forms

Simona Costache, Iuliana Zamfir (2014)

Annales Polonici Mathematici

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B. Y. Chen [Arch. Math. (Basel) 74 (2000), 154-160] proved a geometrical inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature. Recently, this Chen-Ricci inequality was improved in [Int. Electron. J. Geom. 2 (2009), 39-45]. On the other hand, K. Arslan et al. [Int. J. Math. Math. Sci. 29 (2002), 719-726] established a Chen-Ricci inequality for submanifolds, in particular in contact slant submanifolds,...

Minimal submanifolds in 4 with a g.c.K. structure

Marian-Ioan Munteanu (2008)

Czechoslovak Mathematical Journal

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In this paper we obtain all invariant, anti-invariant and C R submanifolds in ( 4 , g , J ) endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.