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.

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.

INVARIANT AND ANTI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2010 ◽  
Vol 07 (03) ◽  
pp. 337-355 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Riemannian Manifolds ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Riemannian Map ◽  
Definition Of ◽  
Totally Real

As a generalization of isometric immersions and Riemannian submersions, Riemannian maps were introduced by Fischer [Riemannian maps between Riemannian manifolds, Contemp. Math.132 (1992) 331–366]. It is known that a real valued Riemannian map satisfies the eikonal equation which provides a bridge between physical optics and geometrical optics. In this paper, we introduce invariant and anti-invariant Riemannian maps between Riemannian manifolds and almost Hermitian manifolds as a generalization of invariant immersions and totally real immersions, respectively. Then we give examples, present a characterization and obtain a geometric characterization of harmonic invariant Riemannian maps in terms of the distributions which are involved in the definition of such maps. We also give a decomposition theorem by using the existence of invariant Riemannian maps to Kähler manifolds. Moreover, we study anti-invariant Riemannian maps, give examples and obtain a classification theorem for umbilical anti-invariant Riemannian maps.

scholarly journals Metallic Kähler and nearly metallic Kähler manifolds

2021 ◽  
pp. 2150146
Author(s):  
Sibel Turanli ◽  
Aydin Gezer ◽  
Hasan Cakicioglu
Keyword(s):  
Riemannian Manifolds ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Linear Connections ◽  
Kähler Structures

In this paper, we construct metallic Kähler and nearly metallic Kähler structures on Riemannian manifolds. For such manifolds with these structures, we study curvature properties. Also, we describe linear connections on the manifold which preserve the associated fundamental 2-form and satisfy some additional conditions and present some results concerning them.

scholarly journals Stability of harmonic maps of Kähler manifolds

1989 ◽  
Vol 30 (2) ◽  
pp. 579-594 ◽  
Author(s):  
D. Burns ◽  
F. Burstall ◽  
P. De Bartolomeis ◽  
J. Rawnsley
Keyword(s):  
Harmonic Maps ◽  
Kähler Manifolds ◽  
Kahler Manifolds
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