Open Access
2019 Sharp Growth Estimates for Warping Functions in Multiply Warped Product Manifolds
Bang-Yen Chen, Shihshu Walter Wei
J. Geom. Symmetry Phys. 52: 27-46 (2019). DOI: 10.7546/jgsp-52-2019-27-46


By applying an average method in PDE, we obtain a dichotomy between “constancy” and “infinity” of the warping functions on complete noncompact Riemannian manifolds for an appropriate isometric immersion of a multiply warped product manifold $N_1\times_{f_2} N_2 \times \cdots \times _{f_k} N_k\, $ into a Riemannian manifold. Generalizing the earlier work of the authors in [9], we establish sharp inequalities between the mean curvature of the immersion and the sectional curvatures of the ambient manifold under the influence of quantities of a purely analytic nature (the growth of the warping functions). Several applications of our growth estimates are also presented.


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Bang-Yen Chen. Shihshu Walter Wei. "Sharp Growth Estimates for Warping Functions in Multiply Warped Product Manifolds." J. Geom. Symmetry Phys. 52 27 - 46, 2019.


Published: 2019
First available in Project Euclid: 26 July 2019

zbMATH: 1427.53046
MathSciNet: MR3931269
Digital Object Identifier: 10.7546/jgsp-52-2019-27-46

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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