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Pythagorean Submanifolds in Euclidean Spaces
In this paper we introduce the notion of a Pythagorean submanifold isometrically immersed into a Euclidean space. This definiton will be based on the...
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A Class of Einstein Submanifolds of Euclidean Space
In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for...
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A Note About a Caffarelli–Kohn–Nirenberg Type Inequality for Euclidean Submanifolds
In the seminal paper, Michael and Simon (Comm Pure Appl Math 26:361–379, 1973) generalized the celebrated Sobolev inequality for submanifolds into...
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Pythagorean Submanifolds
In this paper, we study a particular class of submanifolds, which we call Pythagorean submanifolds, in one of the standard complete simply connected...
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Biconservative Submanifolds with Parallel Normalized Mean Curvature Vector Field in Euclidean Spaces
A submanifold in the Euclidean space is said to have parallel normalized mean curvature vector field if the unit vector field in the direction of the...
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Umehara algebra and complex submanifolds of indefinite complex space forms
The Umehara algebra is studied with motivation on the problem of the non-existence of common complex submanifolds. In this paper, we prove some new...
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Convergence of Martingales with Jumps on Submanifolds of Euclidean Spaces and its Applications to Harmonic Maps
Martingales with jumps on Riemannian manifolds and harmonic maps with respect to Markov processes are discussed in this paper. Discontinuous...
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On the existence of geodesics connecting Lagrangian graphs in Euclidean space
Existence theory for geodesics in the space of Lagrangian submanifolds plays an important role in a program for studying the existence and uniqueness...
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Conformal Kaehler Submanifolds
This paper presents two results in the realm of conformal Kaehler submanifolds. These are conformal immersions of Kaehler manifolds into the standard...
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Rigidity of spacelike LW-submanifolds in the de Sitter space
We establish new rigidity theorems for n -dimensional spacelike linear Weingarten (LW) submanifolds immersed with parallel normalized mean curvature...
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Slant Submanifolds of Conformal Sasakian Space Forms
Chen-Ricci inequality involving Ricci curvature and the squared mean curvature of different kinds of (slant) submanifolds of a conformal Sasakian...
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Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms
This paper aims to establish new upper bounds for the first positive eigenvalue of the Φ-Laplacian operator on Riemannian manifolds in terms of mean...
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Manifolds and Submanifolds Reviewed
We begin with a brief review of differentiable manifolds, vector and tensor fields. Next, we brief on algebra and exterior derivation of differential...
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Conditions for the Parallelism of the Normal Curvature Tensor of Submanifolds
In this paper, sufficient conditions for the parallelism of the normal curvature tensor of submanifolds in spaces of constant curvature are obtained.
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Binary Differential Equations Associated to Congruences of Lines in Euclidean 3-Space
We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential...
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Toward differential geometry of statistical submanifolds
A brief introduction of doubly minimal submanifolds of statistical manifolds is given. A complex submanifold of a holomorphic statistical manifold is...