scholarly journals Deformations of the tangent bundle of projective manifolds

2020 ◽  
Vol 31 (11) ◽  
pp. 2050087
Author(s):  
Thomas Peternell
Keyword(s):  
Projective Space ◽  
Tangent Bundle ◽  
Complex Projective Space ◽  
Projective Manifold ◽  
First Order ◽  
Projective Manifolds ◽  
Complex Projective

We investigate when the tangent bundle of a projective manifold has a nontrivial first-order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.

scholarly journals Geometric applications of critical point theory to submanifolds of complex projective space

1974 ◽  
Vol 55 ◽  
pp. 5-31 ◽  
Author(s):  
Thomas E. Cecil
Keyword(s):  
Projective Space ◽  
Critical Point ◽  
Distance Function ◽  
Complex Projective Space ◽  
Euclidean Distance ◽  
Point Theory ◽  
Euclidean Distance Function ◽  
Complex Projective ◽  
Class Of Functions

In a recent paper, [6], Nomizu and Rodriguez found a geometric characterization of umbilical submanifolds Mn ⊂ Rn+p in terms of the critical point behavior of a certain class of functions Lp, p ⊂ Rn+p, on Mn. In that case, if p ⊂ Rn+p, x ⊂ Mn, then Lp(x) = (d(x,p))2, where d is the Euclidean distance function.

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.

On the dual and hessian mappings of projective hypersurfaces

1987 ◽  
Vol 101 (3) ◽  
pp. 461-468 ◽  
Author(s):  
A. D. R. Choudary ◽  
A. Dimca
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
First Order ◽  
Smooth Hypersurface ◽  
Numerical Invariants ◽  
Dual Mapping ◽  
Complex Projective

We investigate the first-order Thom–Boardman singularity sets of the dual mapping for an arbitrary (and then for a generic) smooth hypersurface in the complex projective space ℙn. Our results focus on nonemptiness, connectedness, regular stratifications and numerical invariants for these sets.

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