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arXiv · 1306.6123

Sasaki manifolds, Kaehler cone manifolds and biharmonic submanifolds

Hajime Urakawa
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Abstract

For a Legendrian submanifold $M$ of a Sasaki manifold $N$, we study harmonicity and biharmonicity of the corresponding Lagrangian cone submanifold C(M) of a Kaehler manifold C(N). We show that, if $C(M)$ is biharmonic in C(N), then it is harmonic; and $M$ is proper biharmonic in $N$ if and only if C(M) has a non-zero eigen-section of the Jacobi operator with the eigenvalue $m=dim M$.

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Hajime Urakawa. 2013-06-26. Sasaki manifolds, Kaehler cone manifolds and biharmonic submanifolds. https://arxiv.org/abs/1306.6123

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