We study “warped Berger” solutions ( S1×S3, G(t) ) of Ricci flow: generalized warped products with the metric induced on each fiber {s}×SU(2) a left-invariant Berger metric. We prove that this structure is preserved by the flow, that these solutions develop finite-time neckpinch singularities, and that they asymptotically approach round product metrics in space-time neighborhoods of their singu...

We analyse a recently constructed class of local solutions of type IIB supergravity that consist of a warped product of AdS3 with a sevendimensional internal space. In one duality frame the only other nonvanishing fields are the NS three-form and the dilaton. We analyse in detail how these local solutions can be extended to globally well-defined solutions of type IIB string theory, with the int...

Recently, we have shown that there do not exist warped product semi-slant submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj Uddin, Balkan J. Geom. Appl. 13 (2008), 55–65]. The nearly cosymplectic structure generalizes the cosymplectic one. Therefore the nearly Kaehler structure generalizes the Kaehler structure in almost Hermitian setting. It is interesting that the warped ...

We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M6, with four-form flux on M6. We show that M6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M6 is a compact, ...