In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the doubly warped product f B ×b F can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections f B ×b F → B and f B ×b F → F , respectively. Some characterizations for non-harmonic biharmonic maps are g...

We study the new warped metric proposed by P. Marcal and Z. Shen. obtain differential equation of such metrics with vanishing Douglas curvature. By solving this equation, we all product metrics. show that Landsberg Berwald are equivalent. classify Ricci-flat Examples included.

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold (cf. Theorem 2.2). Applying this general theory, we obtain basic inequalities involving the Laplacian of the warping function and the squared mean curvature of C-totally real warped product submanifolds of (κ, μ)-space ...

and Applied Analysis 3 where TX and NX are the tangential and normal components of FX, respectively, and for V ∈ T⊥M,

Cosymplectic manifolds provide a natural setting for time dependent mechanical systems as they are locally product of a Kaehler manifold and a one dimensional manifold. Thus study of warped product submanifolds of cosymplectic manifolds is significant. In this paper we have proved results on the non-existence of warped product submanifolds of certain types in cosymplectic manifolds. M.S.C. 2000...

Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends By Pascal Philipp We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type. Our main result is an upper bound on the resonance counting function, with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base ...