Biharmonic submanifolds in metallic Riemannian manifolds

Biharmonic Submanifolds ◽

Complex Surfaces ◽

Metallic Structures ◽

In this paper, we study the biharmonic submanifolds of Riemannian manifolds endowed with metallic and complex metallic structures. In case of both the structures, we obtain the necessary and sufficient conditions for a submanifold to be biharmonic. Particularly, we find the estimates for mean curvature of Lagrangian and complex surfaces.

Biharmonic submanifolds in3-dimensional(κ,μ)-manifolds

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.3575 ◽

2005 ◽

Vol 2005 (22) ◽

pp. 3575-3586 ◽

Cited By ~ 10

Author(s):

K. Arslan ◽

R. Ezentas ◽

C. Murathan ◽

T. Sasahara

Keyword(s):

Riemannian Manifolds ◽

Critical Points ◽

Harmonic Maps ◽

Sufficient Conditions ◽

Biharmonic Maps ◽

Biharmonic Submanifolds ◽

Invariant Surfaces ◽

Legendre Curves ◽

Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of3-dimensional(κ,μ)-manifolds to be biharmonic.

SEMI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887811005725 ◽

2011 ◽

Vol 08 (07) ◽

pp. 1439-1454 ◽

Cited By ~ 6

Author(s):

BAYRAM ṢAHIN

Keyword(s):

Riemannian Manifolds ◽

Sufficient Conditions ◽

Decomposition Theorem ◽

Classification Theorem ◽

Totally Geodesic ◽

Hermitian Manifolds ◽

Almost Hermitian Manifolds ◽

Riemannian Map ◽

This paper has two aims. First, we show that the usual notion of umbilical maps between Riemannian manifolds does not work for Riemannian maps. Then we introduce a new notion of umbilical Riemannian maps between Riemannian manifolds and give a method on how to construct examples of umbilical Riemannian maps. In the second part, as a generalization of CR-submanifolds, holomorphic submersions, anti-invariant submersions, invariant Riemannian maps and anti-invariant Riemannian maps, we introduce semi-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples and investigate the geometry of distributions which are arisen from definition. We also obtain a decomposition theorem and give necessary and sufficient conditions for a semi-invariant Riemannian map to be totally geodesic. Then we study the geometry of umbilical semi-invariant Riemannian maps and obtain a classification theorem for such Riemannian maps.

On some types of lightlike submanifolds of golden semi-Riemannian manifolds

Filomat ◽

10.2298/fil1910231e ◽

2019 ◽

Vol 33 (10) ◽

pp. 3231-3242

Author(s):

Feyza Erdoğan

Keyword(s):

Riemannian Manifolds ◽

Sufficient Conditions ◽

Metric Connection ◽

Necessary And Sufficient ◽

Lightlike Submanifolds

The main purpose of the present paper is to study the geometry of screen transversal lightlike submanifolds and radical screen transversal lightlike submanifolds and screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterizations of screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. Finally, we give two examples.

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

Self θ-congruent minimal surfaces in ℝ3

10.1017/s1446788700002196 ◽

2000 ◽

Vol 69 (2) ◽

pp. 229-244

Author(s):

Weihuan Chen ◽

Yi Fang

Keyword(s):

Minimal Surface ◽

Minimal Surfaces ◽

Mean Curvature ◽

Sufficient Conditions ◽

Rigid Motions ◽

Necessary And Sufficient ◽

Weierstrass Pair

AbstractA minimal surface is a surface with vanishing mean curvature. In this paper we study self θ -congruent minimal surfaces, that is, surfaces which are congruent to their θ-associates under rigid motions in R3 for 0 ≤ θ < 2π. We give necessary and sufficient conditions in terms of its Weierstrass pair for a surface to be self θ-congruent. We also construct some examples and give an application.

SURFACES IN Sn WITH PRESCRIBED GAUSS MAP AND MEAN CURVATURE VECTOR FIELD

International Journal of Mathematics ◽

10.1142/s0129167x06003904 ◽

2006 ◽

Vol 17 (10) ◽

pp. 1127-1143

Author(s):

AYAKO TANAKA

Keyword(s):

Vector Field ◽

Mean Curvature ◽

Sufficient Conditions ◽

Curvature Vector ◽

Gauss Map ◽

Mean Curvature Vector ◽

The Mean ◽

We give relations between the Gauss map and the mean curvature vector field of a surface in the Euclidean unit n-sphere Sn. These relations are necessary and sufficient conditions for the existence of a surface in Sn with prescribed Gauss map and mean curvature vector field. We show that such surfaces can be expressed explicitly by using given data.

Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds

Tohoku Mathematical Journal ◽

10.2748/tmj/1325886291 ◽

2011 ◽

Vol 63 (4) ◽

pp. 855-876 ◽

Cited By ~ 20

Author(s):

Alessio Figalli ◽

Ludovic Rifford ◽

Cédric Villani

Keyword(s):

Riemannian Manifolds ◽

Optimal Transport ◽

Sufficient Conditions ◽

Transport Maps ◽

Semi-Slant Submersions from Almost Product Riemannian Manifolds

Demonstratio Mathematica ◽

10.1515/dema-2016-0029 ◽

2016 ◽

Vol 49 (3) ◽

Cited By ~ 6

Author(s):

Yılmaz Gündüzalp

Keyword(s):

Riemannian Manifolds ◽

Sufficient Conditions ◽

Riemannian Submersion ◽

Totally Geodesic ◽

Definition Of ◽

AbstractIn this paper, we introduce semi-slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give some examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a semi-slant submersion to be totally geodesic.

The scalar curvature of the tangent bundle of a Finsler manifold

Publications de l Institut Mathematique ◽

10.2298/pim1103057b ◽

2011 ◽

Vol 89 (103) ◽

pp. 57-68

Author(s):

Aurel Bejancu ◽

Reda Farran

Keyword(s):

Riemannian Manifold ◽

Scalar Curvature ◽

Riemannian Manifolds ◽

Tangent Bundle ◽

Sufficient Conditions ◽

Finsler Manifold ◽

Finsler Metric ◽

Degree Zero ◽

Let Fm = (M, F) be a Finsler manifold and G be the Sasaki-Finsler metric on the slit tangent bundle TM0 = TM \{0} of M. We express the scalar curvature ?~ of the Riemannian manifold (TM0,G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ?~ to be a positively homogenenous function of degree zero with respect to the fiber coordinates of TM0. Finally, we obtain characterizations of Landsberg manifolds, Berwald manifolds and Riemannian manifolds whose ?~ satisfies the above condition.

Conformal semi-invariant submersions

Communications in Contemporary Mathematics ◽

10.1142/s0219199716500115 ◽

2017 ◽

Vol 19 (02) ◽

pp. 1650011 ◽

Cited By ~ 6

Author(s):

Mehmet Akif Akyol ◽

Bayram Şahin

Keyword(s):

Riemannian Manifolds ◽

Sufficient Conditions ◽

Total Space ◽

Totally Geodesic ◽

Hermitian Manifolds ◽

Almost Hermitian Manifolds ◽

Product Structures ◽

Definition Of ◽

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which arise from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also check the harmonicity of such submersions and find necessary and sufficient conditions of a conformal semi-invariant submersion to be totally geodesic.

The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.