Pseudo-harmonic maps from closed pseudo-Hermitian manifolds to Riemannian manifolds with nonpositive sectional curvature

2018 ◽  
Vol 57 (5) ◽  
Author(s):  
Yibin Ren ◽  
Guilin Yang
Keyword(s):  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Hermitian Manifolds ◽  
Nonpositive Sectional Curvature

ON HARMONIC AND PSEUDOHARMONIC MAPS FROM PSEUDO-HERMITIAN MANIFOLDS

2017 ◽  
Vol 234 ◽  
pp. 170-210 ◽  
Author(s):  
TIAN CHONG ◽  
YUXIN DONG ◽  
YIBIN REN ◽  
GUILIN YANG
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Rigidity Results ◽  
Hermitian Manifolds

In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from pseudo-Hermitian manifolds into Riemannian manifolds or Kähler manifolds. Some foliated results, pluriharmonicity and Siu–Sampson type results are established for both harmonic maps and pseudoharmonic maps.

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.

scholarly journals The balance between existence and nonexistence theorems in differential geometry

2001 ◽  
Vol 32 (1) ◽  
pp. 61-88
Author(s):  
Shihsuh Walter Wei
Keyword(s):  
Differential Geometry ◽  
Sectional Curvature ◽  
Harmonic Maps ◽  
Minimal Submanifolds ◽  
Nonlinear Pde ◽  
Minimal Hypersurfaces ◽  
Nonpositive Sectional Curvature ◽  
Existence And Nonexistence ◽  
Complete Manifolds ◽  
Topological Theorem

We discuss the delicate balance between existence and nonexistence theorems in differential geometry. Studying their interplay yields some information about $ p $-harmonic maps, $ p $-SSU manifolds, geometric $ k_p $-connected manifolds, minimal hypersurfaces and Gauss maps, and manifolds admitting essential positive supersolutions of certain nonlinear PDE. As an application of the theory developed, we obtain a topological theorem for minimal submanifolds in complete manifolds with nonpositive sectional curvature.

A SCHWARZ LEMMA FOR -HARMONIC MAPS AND THEIR APPLICATIONS

2017 ◽  
Vol 96 (3) ◽  
pp. 504-512 ◽  
Author(s):  
QUN CHEN ◽  
GUANGWEN ZHAO
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Schwarz Lemma ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Maps ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Almost Kähler

We establish a Schwarz lemma for $V$-harmonic maps of generalised dilatation between Riemannian manifolds. We apply the result to obtain corresponding results for Weyl harmonic maps of generalised dilatation from conformal Weyl manifolds to Riemannian manifolds and holomorphic maps from almost Hermitian manifolds to quasi-Kähler and almost Kähler manifolds.

Sign in / Sign up

Export Citation Format

Share Document