Sasaki manifolds, Kaehler cone manifolds and biharmonic submanifolds

2013/06/26 by Hajime Urakawa, Urakawa, Hajime
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C43 #msc:58E20 #primary 58E20 #secondary 53C43

paper · pdf · doi:10.48550/arxiv.1306.6123

17 pages

arxiv created 2013/07/08 · arxiv updated 2013/07/10

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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