SLANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2012 ◽  
Vol 10 (02) ◽  
pp. 1250080 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Projective Space ◽  
Riemannian Manifolds ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Sufficient Conditions ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Necessary And Sufficient ◽  
Complex Projective

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficient conditions for slant Riemannian maps to be totally geodesic. Moreover, we relate the notion of slant Riemannian maps to the notion of pseudo horizontally weakly conformal (PHWC) maps which are useful for proving various complex-analytic properties of stable harmonic maps from complex projective space.

SEMI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2011 ◽  
Vol 08 (07) ◽  
pp. 1439-1454 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
Necessary And Sufficient Conditions ◽  
Classification Theorem ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Riemannian Map ◽  
Necessary And Sufficient

This paper has two aims. First, we show that the usual notion of umbilical maps between Riemannian manifolds does not work for Riemannian maps. Then we introduce a new notion of umbilical Riemannian maps between Riemannian manifolds and give a method on how to construct examples of umbilical Riemannian maps. In the second part, as a generalization of CR-submanifolds, holomorphic submersions, anti-invariant submersions, invariant Riemannian maps and anti-invariant Riemannian maps, we introduce semi-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples and investigate the geometry of distributions which are arisen from definition. We also obtain a decomposition theorem and give necessary and sufficient conditions for a semi-invariant Riemannian map to be totally geodesic. Then we study the geometry of umbilical semi-invariant Riemannian maps and obtain a classification theorem for such Riemannian maps.

scholarly journals Semi-invariant Submersions from Almost Hermitian Manifolds

2013 ◽  
Vol 56 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Bayram Ṣahin
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Definition Of ◽  
Necessary And Sufficient

AbstractWe introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semiinvariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.

scholarly journals Conformal semi-invariant submersions

2017 ◽  
Vol 19 (02) ◽  
pp. 1650011 ◽  
Author(s):  
Mehmet Akif Akyol ◽  
Bayram Şahin
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Total Space ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Product Structures ◽  
Definition Of ◽  
Necessary And Sufficient

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which arise from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also check the harmonicity of such submersions and find necessary and sufficient conditions of a conformal semi-invariant submersion to be totally geodesic.

On Kaehler Immersions

1972 ◽  
Vol 24 (6) ◽  
pp. 1178-1182 ◽  
Author(s):  
Koichi Ogiue
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Complex Projective Space ◽  
Holomorphic Sectional Curvature ◽  
Kaehler Manifold ◽  
Totally Geodesic ◽  
Complex Submanifold ◽  
Complex Projective

Let be an (n + p)-dimensional Kaehler manifold of constant holomorphic sectional curvature . B. O'Neill [3] proved the following result.PROPOSITION A. Let M be an n-dimensional complex submanifold immersed in . If and if the holomorphic sectional curvature of M with respect to the induced Kaehler metric is constant, then M is totally geodesic.He also gave the following example: There is a Kaehler imbedding of an w-dimensional complex projective space of constant holomorphic sectional curvature ½ into an -dimensional complex projective space of constant holomorphic sectional curvature 1. This shows that Proposition A is the best possible.

scholarly journals Biharmonic submanifolds in3-dimensional(κ,μ)-manifolds

2005 ◽  
Vol 2005 (22) ◽  
pp. 3575-3586 ◽  
Author(s):  
K. Arslan ◽  
R. Ezentas ◽  
C. Murathan ◽  
T. Sasahara
Keyword(s):  
Riemannian Manifolds ◽  
Critical Points ◽  
Harmonic Maps ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Biharmonic Maps ◽  
Biharmonic Submanifolds ◽  
Invariant Surfaces ◽  
Legendre Curves ◽  
Necessary And Sufficient

Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of3-dimensional(κ,μ)-manifolds to be biharmonic.

scholarly journals Totally real submanifolds in a complex projective space

1999 ◽  
Vol 22 (1) ◽  
pp. 205-208 ◽  
Author(s):  
Liu Ximin
Keyword(s):  
Projective Space ◽  
Scalar Curvature ◽  
Ricci Curvature ◽  
Complex Projective Space ◽  
Minimal Submanifold ◽  
Real Submanifolds ◽  
Totally Geodesic ◽  
Totally Real ◽  
Complex Projective

In this paper, we establish the following result: LetMbe ann-dimensional complete totally real minimal submanifold immersed inCPnwith Ricci curvature bounded from below. Then eitherMis totally geodesic orinf  r≤(3n+1)(n−2)/3, whereris the scalar curvature ofM.

scholarly journals The index of harmonic maps from surfaces to complex projective spaces

2020 ◽  
Vol 31 (09) ◽  
pp. 2050069
Author(s):  
J. Oliver
Keyword(s):  
Projective Space ◽  
Lower Bounds ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Projective Spaces ◽  
Line Bundles ◽  
Complex Projective Spaces ◽  
Holomorphic Sections ◽  
Higher Genus ◽  
Complex Projective

We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.

Sign in / Sign up

Export Citation Format

Share Document