scholarly journals Hermitian harmonic maps from complete Hermitian manifolds to complete Riemannian manifolds

1999 ◽  
Vol 232 (2) ◽  
pp. 331-355 ◽  
Author(s):  
Lei Ni
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Hermitian Manifolds ◽  
Complete Riemannian Manifolds

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.

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.

scholarly journals Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems

2019 ◽  
Vol 372 (3) ◽  
pp. 733-767
Author(s):  
Volker Branding
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Qualitative Behavior ◽  
Quantum Field ◽  
Liouville Theorems ◽  
Dirac Equations ◽  
Monotonicity Formulas ◽  
Curvature Term ◽  
Nonlinear Dirac Equations ◽  
Complete Riemannian Manifolds

Abstract We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.

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