scholarly journals New results on derivatives of the shape operator of a real hypersurface in a complex projective space

2021 ◽  
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Shape Operator ◽  
Complex Projective ◽  
Derivatives Of

scholarly journals Lie Derivatives of the Shape Operator of a Real Hypersurface in a Complex Projective Space

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Juan de Dios Pérez ◽  
David Pérez-López
Keyword(s):  
Differential Operator ◽  
Projective Space ◽  
Tensor Field ◽  
Complex Projective Space ◽  
Shape Operator ◽  
Symmetric Tensor ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Complex Projective ◽  
Derivatives Of

AbstractWe consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated with the generalized Tanaka–Webster connection we can define a differential operator of first order. For any nonnull real number k and any symmetric tensor field of type (1,1) B on M, we can define a tensor field of type (1,2) on M, $$B^{(k)}_T$$ B T ( k ) , related to Lie derivative and such a differential operator. We study symmetry and skew symmetry of the tensor $$A^{(k)}_T$$ A T ( k ) associated with the shape operator A of M.

scholarly journals A MINIMAL REAL HYPERSURFACE OF A COMPLEX PROJECTIVE SPACE WITH NONNEGATIVE SECTIONAL CURVATURE

2010 ◽  
Vol 81 (3) ◽  
pp. 488-492
Author(s):  
MAYUKO KON
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Nonnegative Sectional Curvature ◽  
Complex Projective

AbstractWe give a characterization of a minimal real hypersurface with respect to the condition for the sectional curvature.

scholarly journals REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE

2010 ◽  
Vol 53 (2) ◽  
pp. 347-358 ◽  
Author(s):  
SADAHIRO MAEDA ◽  
HIROO NAITOH
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Shape Operator ◽  
Type A ◽  
Real Hypersurfaces ◽  
Ruled Real Hypersurfaces ◽  
Shape Operators ◽  
Complex Projective ◽  
Invariant Shape

AbstractWe characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.

scholarly journals Real hypersurfaces of a complex projective space II

1984 ◽  
Vol 30 (1) ◽  
pp. 123-127 ◽  
Author(s):  
Sadahiro Maeda
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Complex Projective

We consider a certain real hypersurface M of a complex projective space. The purpose of this paper is to characterize M in terms of Ricci curvatures.

Additive Riemann–Hilbert Problem in Line Bundles Over ℂℙ1

2006 ◽  
Vol 49 (1) ◽  
pp. 72-81 ◽  
Author(s):  
Roman J. Dwilewicz
Keyword(s):  
Line Bundle ◽  
Projective Space ◽  
Complex Projective Space ◽  
Real Hypersurface ◽  
Hilbert Problem ◽  
Holomorphic Functions ◽  
Riemann Function ◽  
Line Bundles ◽  
Complex Projective ◽  
Riemann Hilbert Problem

AbstractIn this note we consider -problem in line bundles over complex projective space ℂℙ1 and prove that the equation can be solved for (0, 1) forms with compact support. As a consequence, any Cauchy-Riemann function on a compact real hypersurface in such line bundles is a jump of two holomorphic functions defined on the sides of the hypersurface. In particular, the results can be applied to ℂℙ2 since by removing a point from it we get a line bundle over ℂℙ1.

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