Asian Journal of Mathematics

On the existence of pseudoharmonic maps from pseudohermitian manifolds into Riemannian manifolds with nonpositive sectional curvature

Shu-Cheng Chang and Ting-Hui Chang

Full-text: Open access

Abstract

In this paper, we first derive a CR Bochner identity for the pseudoharmonic map heat flow on pseudohermitian manifolds. Secondly, we are able to prove existence of the global solution for the pseudoharmonic map heat flow from a closed pseudohermitian manifold into a Riemannian manifold with nonpositive sectional curvature. In particular, we prove the existence theorem of pseudoharmonic maps. This is served as the CR analogue of Eells-Sampson’s Theorem for the harmonic map heat flow.

Article information

Source
Asian J. Math., Volume 17, Number 1 (2013), 1-16.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1383923433

Mathematical Reviews number (MathSciNet)
MR3038722

Zentralblatt MATH identifier
1304.32024

Subjects
Primary: 32V05: CR structures, CR operators, and generalizations 32V20: Analysis on CR manifolds
Secondary: 53C56: Other complex differential geometry [See also 32Cxx]

Keywords
CR Bochner identity energy density pseudoharmonic map pseudoharmonic map heat flow pseudohermitian manifold pseudohermitian Ricci tensors pseudohermitian torsion sub-Laplacian Folland-Stein space

Citation

Chang, Shu-Cheng; Chang, Ting-Hui. On the existence of pseudoharmonic maps from pseudohermitian manifolds into Riemannian manifolds with nonpositive sectional curvature. Asian J. Math. 17 (2013), no. 1, 1--16. https://projecteuclid.org/euclid.ajm/1383923433


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