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This note is a continuation of the paper [2] (see references). We describe some natural pseudogroup structures on almost complex manifolds of type $m$. A kind of coherency is discussed for the sheaf of almost holomorphic functions.

Complex Variables · Mathematics 2007-05-23 S. Dimiev

In this paper, we induce a semi-Riemannian metric on the $r$-null submanifold. We establish the links between the null geometry and basics invariants of the associated semi-Riemannian geometry on $r$-null submanifold and semi-Riemannian…

General Mathematics · Mathematics 2021-12-15 Ménédore Karimumuryango , Domitien Ndayirukiye , Gilbert Nibaruta , Aboubacar Nibirantiza

In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…

Differential Geometry · Mathematics 2020-09-24 Eder M. Correa

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…

Differential Geometry · Mathematics 2026-03-10 Philip Boalch

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

Differential Geometry · Mathematics 2009-07-14 Dimitar Mekerov

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions…

Differential Geometry · Mathematics 2015-05-20 Marie-Amelie Lawn , Miguel Ortega

We prove the existence of a one parameter family of minimal embedded hypersurfaces in $R^{n+1}$, for $n \geq 3$, which generalize the well known 2 dimensional "Riemann minimal surfaces". The hypersurfaces we obtain are complete, embedded,…

Differential Geometry · Mathematics 2007-05-23 S. Kaabachi , F. Pacard

In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…

Differential Geometry · Mathematics 2023-10-23 Barbara Opozda

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,…

Differential Geometry · Mathematics 2014-05-19 Yoshiaki Maeda , Steven Rosenberg , Fabián Torres-Ardila

An (I,J,K)-generalized Finsler structure on a 3-manifold is a generalization of a Finslerian structure, introduced in order to separate and clarify the local and global aspects in Finsler geometry making use of the Cartan's method of…

Differential Geometry · Mathematics 2012-07-09 Sorin V. Sabau , Kazuhiro Shibuya , Gheorghe Pitis

We derive general structure and rigidity theorems for submetries $f: M \to X$, where $M$ is a Riemannian manifold with sectional curvature $\sec M \ge 1$. When applied to a non-trivial Riemannian submersion, it follows that $diam X \leq…

Differential Geometry · Mathematics 2014-04-16 Xiaoyang Chen , Karsten Grove

We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…

Geometric Topology · Mathematics 2011-10-07 Clayton Shonkwiler , David Shea Vela-Vick

We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…

Complex Variables · Mathematics 2024-02-28 Norbert A'Campo , Athanase Papadopoulos

In this article, we consider the almost Hermitian structure on $TM$ induced by a pair of a metric and an affine connection on $M$. We find the conditions under which $TM$ admits almost K\"ahler structures, K\"ahler structures and Einstein…

Differential Geometry · Mathematics 2025-03-24 Hiroyasu Satoh

We propose a generalization of two classes of Lie-Hamilton systems on the Euclidean plane to two-dimensional curved spaces, leading to novel Lie-Hamilton systems on Riemannian spaces (flat $2$-torus, product of hyperbolic lines, sphere and…

Mathematical Physics · Physics 2024-11-26 Rutwig Campoamor-Stursberg , Oscar Carballal , Francisco J. Herranz

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we…

Differential Geometry · Mathematics 2012-11-14 Christof Puhle

On a manifold with an almost contact metric structure $(\varphi,\vec\xi,\eta,g,X,D)$ the notions of the interior and the $N$-prolonged connections are introduced. Using the $N$-prolonged connection, a new almost contact metric structure is…

Differential Geometry · Mathematics 2015-06-08 Sergey V. Galaev

In this paper, we obtain a sufficient and necessary condition for a simply connected Riemannian manifold $(M^n, g)$ to be isometrically immersed, as a submanifold with codimension $p\geq 1$, into the product $S^k\times H^{n+p-k}$ of sphere…

Differential Geometry · Mathematics 2013-11-18 Xingxiao Li , Tianqun Zhang

We introduce a notion of quasiconvexity for continuous functions $f$ defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold $(M,g)$ and $\mathbb{R}^m$, naturally generalizing the classical…

Analysis of PDEs · Mathematics 2026-04-21 Aurora Corbisiero , Chiara Leone , Carlo Mantegazza

In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds,…

Differential Geometry · Mathematics 2019-12-12 Xiuxiu Cheng , Zejun Hu , Marilena Moruz , Luc Vrancken