Bochner-type formulas for transversally harmonic maps

Qun Chen; Wubin Zhou

doi:10.1142/S0129167X11007471

Bochner-type formulas for transversally harmonic maps

Qun Chen^*, Wubin Zhou

^*Corresponding author for this work

Wuhan University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The main purpose of this paper is to study the properties of transversally harmonic maps by using Bochner-type formulas. As an application, we obtain the following theorem between compact Sasaki manifolds: Let f be a transversally harmonic map from compact Sasaki manifold M to compact Sasaki manifold M′, and M′ has a strongly negative transverse curvature. If the rank of d _Tf is at least three at some points of M, then f is contact holomorphic (or contact anti-holomorphic).

Original language	English
Article number	1250003
Journal	International Journal of Mathematics
Volume	23
Issue number	3
DOIs	https://doi.org/10.1142/S0129167X11007471
Publication status	Published - Mar 2012
Externally published	Yes

Keywords

Bochner formula
Riemannian foliation
Sasaki geometry
transversally harmonic maps

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10.1142/S0129167X11007471

Cite this

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abstract = "The main purpose of this paper is to study the properties of transversally harmonic maps by using Bochner-type formulas. As an application, we obtain the following theorem between compact Sasaki manifolds: Let f be a transversally harmonic map from compact Sasaki manifold M to compact Sasaki manifold M′, and M′ has a strongly negative transverse curvature. If the rank of d Tf is at least three at some points of M, then f is contact holomorphic (or contact anti-holomorphic).",

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AB - The main purpose of this paper is to study the properties of transversally harmonic maps by using Bochner-type formulas. As an application, we obtain the following theorem between compact Sasaki manifolds: Let f be a transversally harmonic map from compact Sasaki manifold M to compact Sasaki manifold M′, and M′ has a strongly negative transverse curvature. If the rank of d Tf is at least three at some points of M, then f is contact holomorphic (or contact anti-holomorphic).

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KW - Riemannian foliation

KW - Sasaki geometry

KW - transversally harmonic maps

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Bochner-type formulas for transversally harmonic maps

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Keywords

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