We classify all closed non-orientable P-irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with complexity 6 (the four flat ones and the filling of the Gieseking manifold, which is of type Sol), and three with complexity 7 (one manifold of type Sol, and t...

Abstract We show that any compact metric f - K -contact, respectively S -manifold is obtained from a Sasakian manifold by an iteration of constructions mapping tori, rotations, and type II deformations.

The article deals with nearly Sasakian manifolds of a constant type. It is proved that the almost Hermitian structure induced on integral maximum dimension first fundamental distribution manifold Kähler manifold. class zero type coincides manifolds. concept constancy an contact metric introduced through its Nijenhuis tensor, and criterion proved. coincidence both concepts for structure.

We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C∗-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the K-theoretic index classes, which we use to generalize the product formula for the topological signature to higher signatures.

The object of this paper is to define and study a new type of non-flat Riemannian manifold called nearly Einstein manifold. The notion of this nearly Einstein manifold has been established by an example and an existence theorem. Some geometric properties are obtained. AMS Mathematics Subject Classification (2010): 53C25.

We study the structure of warped compactifications of type IIB string theory to six space–time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kähler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi–Yau.  2004 Elsevier B.V. All rights reserved.

We study the topology of a complete asymptotically hyperbolic Einstein manifold such that its conformal boundary has positive Yamabe invariant. We proved that all maps from such manifold into any nonpositively curved manifold are homotopically trivial. Our proof is based on a Bochner type argument on harmonic maps.