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Integral geometry of complex space forms
Integral geometry complex space forms Differential Geometry
2012/4/18
Using the language of Alesker's theory of valuations on manifolds, a thorough account of the integral geometry of the complex space forms is given. The local kinematic formulas on complex space forms ...
Special Lagrangian 4-folds with $SO(2)\rtimes S_3$-Symmetry in Complex Space Forms
Lagrangian 4-folds Complex Space Forms Differential Geometry
2011/8/25
Abstract: In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an $SO(2)\rtimes S_3$-symmetry on the second fundamental form. The algebraic s...
CR submanifolds of maximal CR dimension of a complex space form with recurrent shape operator
Complex space form CR submanifold of maximal CR dimension
2011/2/28
Let M be a CR submanifold of maximal CR dimension of a complex space form M. The shape operator A of the distinguished vector field is recurrent if there exists a 1-form v such that ∇A = A X...
Non-existence of CR submanifolds of maximal CR dimension satisfying RA = 0 in non-flat complex space forms
Complex space form CR submanifold of maximal CR dimension
2011/2/25
It has been proved that there are no real hypersurfaces satisfying RA =0 in non-flat complex space forms. In this paper we prove that the same is true in the case of CR submanifolds of maximal CR dime...
Geometry of CR submanifolds of maximal CR dimension in complex space forms
Complex space form CR submanifold of maximal CR dimension
2011/2/24
On real hypersurfaces in complex space forms many results are proven.In this paper we generalize some results concerning extrinsic geometry of real hypersurfaces, to CR submanifolds of maximal CR dime...
Minimal Lagrangian submanifolds in indefinite complex space
Lagrangian submanifolds complex space
2010/11/22
Consider the complex linear space C^n endowed with the natural pseudo-Hermitian form <<.,.>>_p of signature p. This yields both a pseudo-Riemannian and a symplectic structure on C^n. We prove that th...
Kaehler immersions of homogeneous Kaehler manifolds into complex space forms
Kä hler metrics infinite dimensional complex space forms
2010/12/9
In this paper we study the homogeneous Kähler manifolds (h.K.m.) which can be Kähler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the
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Shape Operator AH for Slant Submanifolds in Generalized Complex Space Forms
Shape operator slant submanifolds generalized complex space form k-Ricci curvature
2010/2/26
In this article, we establish an inequality between the sectional curvature function K and the shape operator AH at the mean curvature vector for slant submanifolds in generalized complex space forms....