We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto’s Theorem on product of almost contact manifolds to flat bundles. We construct some examples on Boothby–Wang fibrations over contact-symplectic manifolds. In p...

In this short paper we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result Böhm and Wilking have for dimensions twelve and above. Moreover, the manifolds constructed here are...

The theory of inhomogeneous Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the Groshev type theory is established for all such manifolds. Our results naturally incorporate and generalize the homogeneous measure and dimension theorems for non-degenerate manifolds established to date. The results have natur...

We investigate when two generalized real Bott manifolds of height 2 have isomorphic cohomology rings with Z/2 coefficients and also when they are diffeomorphic. It turns out that cohomology rings with Z/2 coefficients do not distinguish those manifolds up to diffeomorphism in general. This gives a counterexample to the cohomological rigidity problem for real toric manifolds posed in [5]. We als...

mulas §1.5. Multiplicity-free representations — definition §2. Multiplicity-free theorem — general framework §2.1. Holomorphic bundles and anti-holomorphic maps §2.2. Multiplicity-free theorem — line bundle case §2.3. Geometry on the base space D §2.4. Multiplicity-free theorem — vector bundle case §3. Visible actions on complex manifolds §3.1. Previsible and visible actions on complex manifold...

In an earlier paper [1], the author introduced the notion of convolution of Riemannian manifolds. In [1] he also provided some examples and applications of convolution manifolds. In this paper we use tensor product to construct more examples of convolution manifolds and investigate fundamental properties of convolution manifolds. In particular, we study the relationship between convolution mani...

We continue the study, begun in [Ru], of secant defective manifolds having “simple entry loci”. We prove that such manifolds are rational and describe them in terms of tangential projections. Using also [IR], their classification is reduced to the case of Fano manifolds of high index, whose Picard group is generated by the hyperplane section class. Conjecturally, the former should be linear sec...

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in [18]. Specifically, we establish a non-vanishing result for the invariants of symplectic four-manifolds, which leads to new proofs of the indecomposability theorem for symplectic four-manifolds and the symplectic Tho...

Orientable 4-dimensional infrasolvmanifolds bound orientably. We show that every non-orientable 4-dimensional infrasolvmanifold M with β = β1(M ;Q) > 0 or with geometry Nil 4 or Sol3×E1 bounds. However there are Sol 1 -manifolds which are not boundaries. The question remains open for Nil × E-manifolds. Any possible counter-examples have severely constrained fundamental groups. We also find simp...

We develop a family of infinite-dimensional (i.e. non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Ck b with respect to appropriate reference measures. The case k = ∞, in which the manifolds are modelled on Fréchet spaces, is included. The manifolds admit the Fisher-Rao metric and the dually flat geometry of Amari...