Related papers: Homogeneous structures of $3$-dimensional Sasakian…

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space, de Sitter 3-space, and Minkowski motion group is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a…

Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are…

We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

This paper provides a topological method for filling contact structures on the connected sums of $S^2\times S^3$. Examples of nonsymplectomorphic strong fillings of homotopy equivalent contact structures with vanishing first Chern class on…

In this note, we show a uniqueness result of homogeneous quasimorphisms defined on the universal cover of the symplectic linear group.

We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown…

We show that a Lorentzian homogeneous space admitting a homogeneous structure of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous plane wave.

Explicit formulae for homogenous Ricci solitons on three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces are obtained.

Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dimensional shapes represented by triangular meshes of a given…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

This paper introduces the notion of $k$-isoparametric hypersurface in an $(n+1)$-dimensional Riemannian manifold for $k=0,1,...,n$. Many fundamental and interesting results (towards the classification of homogeneous hypersurfaces among…

We introduce a global Cauchy-Riemann($CR$)-invariant and discuss its behavior on the moduli space of $CR$-structures. We argue that this study is related to the Smale conjecture in 3-topology and the problem of counting complex structures.…

We introduce the notion of abelian almost contact structures on an odd dimensional real Lie algebra $\mathfrak g$. This a sufficient condition for the structure to be normal. We investigate correspondences with even dimensional real Lie…

The Hamiltonian analysis for a 3-dimensional connection dynamics of $\frak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01}, L_{02}, L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the…

In this paper we classify those three-dimensional Riemannian Lie groups which admit harmonic morphisms to surfaces.

Koll\'ar has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In…

This paper begins the study of relations between Riemannian geometry and contact topology in any dimension and continues this study in dimension 3. Specifically we provide a lower bound for the radius of a geodesic ball in a contact…

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in…