scholarly journals Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2125
Author(s):  
Cristina E. Hretcanu ◽  
Adara M. Blaga
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Euclidean Spaces ◽  
Slant Submanifolds

In the present paper, we study some properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and we construct examples in Euclidean spaces. Additionally, we study some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.

scholarly journals Warped product pointwise pseudo-slant submanifolds of locally product Riemannian manifolds

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 423-438 ◽  
Author(s):  
Lamia Alqahtani ◽  
Siraj Uddina
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Form ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Characterization Theorem ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Equality Case ◽  
Slant Submanifolds ◽  
The Second Fundamental Form

In [3], it was shown that there are no warped product submanifolds of a locally product Riemannian manifold such that the spherical submanifold of a warped product is proper slant. In this paper, we introduce the notion of warped product submanifolds with a slant function and show that there exists a class of non-trivial warped product submanifolds of a locally product Riemannian manifold such that the spherical submanifold is pointwise slant by giving some examples. We present a characterization theorem and establish a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant function for such warped product submanifolds of a locally product Riemannian manifold. The equality case is also considered.

scholarly journals Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2467
Author(s):  
Cristina E. Hretcanu ◽  
Adara M. Blaga
Keyword(s):  
Riemannian Manifolds ◽  
Warped Product ◽  
Slant Submanifolds ◽  
Short Survey ◽  
Existence And Nonexistence ◽  
Invariant Submanifolds

We provide a brief survey on the properties of submanifolds in metallic Riemannian manifolds. We focus on slant, semi-slant and hemi-slant submanifolds in metallic Riemannian manifolds and, in particular, on invariant, anti-invariant and semi-invariant submanifolds. We also describe the warped product bi-slant and, in particular, warped product semi-slant and warped product hemi-slant submanifolds in locally metallic Riemannian manifolds, obtaining some results regarding the existence and nonexistence of non-trivial semi-invariant, semi-slant and hemi-slant warped product submanifolds. We illustrate all these by suitable examples.

scholarly journals The geometry of warped product singularities

2017 ◽  
Vol 14 (02) ◽  
pp. 1750024 ◽  
Author(s):  
Ovidiu Cristinel Stoica
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Big Bang ◽  
Warping Function ◽  
Warped Products ◽  
Riemann Curvature ◽  
The Big Bang

In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry

2002 ◽  
Vol 45 (3) ◽  
pp. 378-387
Author(s):  
Manuel Fernández-López ◽  
Eduardo García-Río ◽  
Demir N. Kupeli
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Warped Product ◽  
Product Structure ◽  
Twisted Product ◽  
Partial Differential ◽  
Decomposition Theorems

AbstractA partial differential equation, the local Möbius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local Möbius equation and an additional partial differential equation.

SLANT SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS

2013 ◽  
Vol 10 (10) ◽  
pp. 1350058 ◽  
Author(s):  
GÜLŞAH AYDIN ◽  
A. CEYLAN ÇÖKEN
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Slant Submanifold ◽  
Slant Submanifolds ◽  
Lightlike Submanifold

In this study, we search slant submanifolds of almost product semi-Riemannian manifold. Accordingly, we investigate slant submanifolds of semi-Riemannian manifold by making the classifications as slant Riemannian, slant semi-Riemannian and slant lightlike submanifold. Moreover, we add the theorems which characterize existence of slant submanifold.

scholarly journals Warped product submanifolds in metallic Riemannian manifolds

2020 ◽  
Vol 51 (3) ◽  
pp. 161-186
Author(s):  
Cristina Elena Hretcanu ◽  
Adara Blaga
Keyword(s):  
Riemannian Manifolds ◽  
Warped Product ◽  
Euclidean Spaces

In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic and Golden Riemannian manifolds. Also, we provide some examples of warped product submanifolds in Euclidean spaces.

scholarly journals Remarks on metallic warped product manifolds

2018 ◽  
Vol 33 (2) ◽  
pp. 269
Author(s):  
Adara-Monica Blaga ◽  
Cristina-Elena Hretcanu
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Metallic Structure ◽  
Necessary And Sufficient

We characterize the metallic structure on the product of two metallic manifolds in terms of metallic maps and provide a necessary and sufficient condition for the warped product of two locally metallic Riemannian manifolds to be locally metallic. The particular case of product manifolds is discussed and an example of metallic warped product Riemannian manifold is provided.

Riemannian manifolds whose curvature operator R(X, Y) has constant eigenvalues

2004 ◽  
Vol 70 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Y. Nikolayevsky
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Riemannian Manifolds ◽  
Warped Product ◽  
Curvature Operator ◽  
Specific Function ◽  
3 Dimensional ◽  
Space Of Constant Curvature

A Riemannian manifold Mn is called IP, if, at every point x ∈ Mn, the eigenvalues of its skew-symmetric curvature operator R(X, Y) are the same, for every pair of orthonormal vectors X, Y ∈ TxMn. In [5, 6, 12] it was shown that for all n ≥ 4, except n = 7, an IP manifold either has constant curvature, or is a warped product, with some specific function, of an interval and a space of constant curvature. We prove that the same result is still valid in the last remaining case n = 7, and also study 3-dimensional IP manifolds.

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