Mok-Siu-Yeung type formulas on contact locally sub-symmetric spaces

Petit, Robert

doi:10.1007/s10455-008-9120-1

Cited by 6 publications

(8 citation statements)

References 35 publications

(71 reference statements)

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“…In [6], Petit derived the first variation formula of the energy E H, H and call a critical point of E H, H a pseudoharmonic map. Note that there is an extra condition on the pull-back of the pseudo-Hermitian torsion.…”

Section: Basic Notionsmentioning

confidence: 99%

“…Then we have Proposition 3.1. ( [1],cf also [6]) For any horizontal vector field ν ∈ Γ(f −1 H(N )), let {f t }(|t| < ε) with f 0 = f and ν = ∂ft ∂t | t=0 be a one parameter variation . Then we have…”

Section: Basic Notionsmentioning

confidence: 99%

“…As we have mentioned, the notion of pseudoharmonic maps is slightly different from that in [6]. In [1], the author has shown that Petit's pseudoharmonic maps coincide with Dong's if the target manifold is Sasakian.…”

Section: Basic Notionsmentioning

confidence: 99%

“…For example, some pseudoharmonic maps were introduced in the field of pseudo-Hermitian geometry (cf. [1], [2], [6]). For a map f : (M 2m+1 , H(M ), J, θ) → (N, H(N ), J, θ) between two pseudo-Hermian maps, Petit [6] introduced a new horizontal energy functional E H, H (f ).…”

Section: Introductionmentioning

confidence: 99%

“…[1], [2], [6]). For a map f : (M 2m+1 , H(M ), J, θ) → (N, H(N ), J, θ) between two pseudo-Hermian maps, Petit [6] introduced a new horizontal energy functional E H, H (f ). He derived the first variation formula of E H, H (f ) and called a critical point of the energy a pseudoharmonic map.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Harmonic and Pseudoharmonic Maps From Pseudo-Hermitian Manifolds

Tian¹,

Ye²,

Ren³

et al. 2017

Nagoya Math. J.

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In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed submanifold in Heisenberg group, we give some conditions on Weingarten maps to obtain some unstability of pseudoharmonic maps between these pseudo-Hermitian manifolds.

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Section: Basic Notionsmentioning

confidence: 99%

Section: Basic Notionsmentioning

confidence: 99%

Section: Basic Notionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Harmonic and Pseudoharmonic Maps From Pseudo-Hermitian Manifolds

Tian¹,

Ye²,

Ren³

et al. 2017

Nagoya Math. J.

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An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion

Ivanov

Vassilev²

2012

J. Geom.

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We prove a CR Obata type result that if the first positive eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex pseudohermitian manifold with a divergence free pseudohermitian torsion takes the smallest possible value then, up to a homothety of the pseudohermitian structure, the manifold is the standart Sasakian unit sphere. We also give a version of this theorem using the existence of a function with traceless horizontal Hessian on a complete, with respect to Webster's metric, pseudohermitian manifold.

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