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Title: Optimal inequalities for multiply warped product submanifolds
Authors: Chen, Bang-Yen *
Dillen, Franki * # ×
Issue Date: 2008
Series Title: International Electronic Journal of Geometry vol:1 issue:1 pages:1-11
Abstract: In an earlier paper [3] the first author proved that for any isometric immersion of a warped product N_1 x_f N_2 into a Riemannian m-manifold of constant sectional curvature c, the warping function f satisfies the optimal general inequality:
\frac {\Delta f}{f} \leq \frac{(n_1 + n_2)^2}{4n_2} H^2 + n_1c,
where $n_i = dim N_i, i = 1,2, H^2 is the squared mean curvature, and \Delta is the Laplacian operator of N_1. Moreover, he proved in [2] that for a CR-warped product N_T \times_f N_\perp in a Kaehler manifold, the second fundamental form h satisfies ||h||^2 \geq 2n_2 || \nabla (ln f)||^2, where n_2 = dim N_\perp. In this article we extend these inequalities to multiply warped product manifolds in an arbitrary Riemannian or Kaehlerian manifold. We also provide some examples to illustrate that our results are sharp. Moreover, several applications are also obtained.
ISSN: 1307-5624
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
* (joint) first author
× corresponding author
# (joint) last author

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