Related papers: Half-dimensional immersions into the para-complex …

In this paper we investigate surfaces in $\mathbb C P^2$ without complex points and characterize the minimal surfaces without complex points and the minimal Lagrangian surfaces by Ruh-Vilms type theorems. We also discuss the liftability of…

We prove a stability result of isometric immersions of hypersurfaces in Riemannian manifolds, with respect to $L^p$-perturbations of their fundamental forms: For a manifold $M^d$ endowed with a reference metric and a reference shape…

Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost…

We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian…

The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with…

Given a compact manifold $M$ and a Riemannian manifold $N$ of bounded geometry, we consider the manifold ${\rm Imm} (M,N)$ of immersions from $M$ to $N$ and its subset ${\rm Imm}_\mu (M,N)$ of those immersions with the property that the…

Let $M$ and $N$ be connected manifolds without boundary with $\dim(M) < \dim(N)$, and let $M$ compact. Then shape space in this work is either the manifold of submanifolds of $N$ that are diffeomorphic to $M$, or the orbifold of…

In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values in $\mathbb R^3$ satisfying certain boundary conditions at the…

In this note, we give natural extensions to cylinders and tori of a classical result due to T. Takahashi about minimal immersions into spheres. More precisely, we deal with Euclidean isometric immersions whose projections in R^N satisfy a…

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various…

An isometric immersion $x:M^n\rightarrow S^{n+p}$ is called Willmore if it is an extremal submanifold of the Willmore functional: $W(x)=\int_{M^n} (S-nH^2)^{\frac{n}{2}}dv$, where $S$ is the norm square of the second fundamental form and…

In this paper, we study harmonic Riemannian submersions from 3-dimensional geometries using the ( generalized) integrability data associated to an orthonormal frame natural to a Riemannian submersion. We give complete classifications of…

We study exact Lagrangian immersions with one double point of a closed orientable manifold K into n-complex-dimensional Euclidean space. Our main result is that if the Maslov grading of the double point does not equal 1 then K is homotopy…

The main purpose of the paper is twofold: First, to extend a well known theorem of Ruh-Vilms in the Euclidean space to symmetric spaces and, secondly, to apply this result to extend Hoffman-Osserman-Schoen Theorem (HOS Theorem) to…

We study the second fundamental form of semi-isometric CR immersions from strictly pseudoconvex CR manifolds into K\"ahler manifolds. As an application, we give a precise condition for the CR umbilicality of real hypersurfaces, extending an…

We explore the relation among volume, curvature and properness of a $m$-dimensional isometric immersion in a Riemannian manifold. We show that, when the $L^p$-norm of the mean curvature vector is bounded for some $m \leq p\leq \infty$, and…

We offer an alternative approach to the asymptotic rigidity of codimension-1 isometric immersions via quantitative rigidity estimates. We show that an immersion between compact manifolds $M$ and $N$ of dimensions $d$ and $d + 1$,…

This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then we…

Let $M$ be an open Riemann surface. It was proved by Alarc\'on and Forstneri\v{c} (arXiv:1408.5315) that every conformal minimal immersion $M\to\mathbb R^3$ is isotopic to the real part of a holomorphic null curve $M\to\mathbb C^3$. In this…

In this paper we study biconservative immersions into the semi-Riemannian space form $R^4_2(c)$ of dimension 4, index 2 and constant curvature, where $c\in\{0,-1,1\}$. First, we obtain a characterization of quasi-minimal proper…