scholarly journals Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 692 ◽  
Author(s):  
Shandra ◽  
Mikeš
Keyword(s):  
Jordan Algebra ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Basic Type ◽  
System Of Equations ◽  
Special Jordan Algebra ◽  
Type Form

In the present paper, we study geodesic mappings of special pseudo-Riemannian manifolds called V n ( K ) -spaces. We prove that the set of solutions of the system of equations of geodesic mappings on V n ( K ) -spaces forms a special Jordan algebra and the set of solutions generated by concircular fields is an ideal of this algebra. We show that pseudo-Riemannian manifolds admitting a concircular field of the basic type form the class of manifolds closed with respect to the geodesic mappings.

Newton’s method for approximating zeros of vector fields on Riemannian manifolds

2008 ◽  
Vol 29 (1-2) ◽  
pp. 417-427 ◽  
Author(s):  
Ioannis K. Argyros ◽  
Saïd Hilout
Keyword(s):  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Vector Fields

Jacobi fields and geodesic spheres

1979 ◽  
Vol 82 (3-4) ◽  
pp. 233-240 ◽  
Author(s):  
L. Vanhecke ◽  
T. J. Willmore
Keyword(s):  
Sectional Curvature ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Holomorphic Sectional Curvature ◽  
Principal Curvatures ◽  
Jacobi Fields ◽  
Geodesic Spheres ◽  
Jacobi Vector ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds

SynopsisThis is a contribution to the general problem of determining the extent to which the geometry of a riemannian manifold is determined by properties of its geodesic spheres. In particular we show that total umbilicity of geodesic spheres determines riemannian manifolds of constant sectional curvature; quasi-umbilicity of geodesic spheres determines Kähler and nearly-Kähler manifolds of constant holomorphic sectional curvature; and the condition that geodesic spheres have only two different principal curvatures, one having multiplicity 3, determines manifolds locally isometric to the quaternionic projective spaces. The use of Jacobi vector fields leads to a unified treatment of these different cases.

scholarly journals Killing vector fields of constant length on Riemannian manifolds

2008 ◽  
Vol 49 (3) ◽  
pp. 395-407 ◽  
Author(s):  
V. N. Berestovskii ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Manifolds ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Constant Length

scholarly journals Classification of Ricci solitons on Euclidean hypersurfaces

2014 ◽  
Vol 25 (11) ◽  
pp. 1450104 ◽  
Author(s):  
Bang-Yen Chen ◽  
Sharief Deshmukh
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Potential Field ◽  
Vector Fields ◽  
Ricci Soliton ◽  
Position Vector ◽  
Ricci Solitons ◽  
Euclidean Submanifolds

A Ricci soliton (M, g, v, λ) on a Riemannian manifold (M, g) is said to have concurrent potential field if its potential field v is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in [Ricci solitons and concurrent vector fields, preprint (2014), arXiv:1407.2790]. The most important concurrent vector field is the position vector field on Euclidean submanifolds. In this paper we completely classify Ricci solitons on Euclidean hypersurfaces arisen from the position vector field of the hypersurfaces.

scholarly journals Einstein Finsler metrics and killing vector fields on Riemannian manifolds

2016 ◽  
Vol 60 (1) ◽  
pp. 83-98 ◽  
Author(s):  
XinYue Cheng ◽  
ZhongMin Shen
Keyword(s):  
Riemannian Manifolds ◽  
Vector Fields ◽  
Killing Vector ◽  
Finsler Metrics ◽  
Killing Vector Fields

scholarly journals Riemannian manifolds with many Killing vector fields

1980 ◽  
Vol 105 (3) ◽  
pp. 241-247 ◽  
Author(s):  
Ann Stehney ◽  
Richard Millman
Keyword(s):  
Riemannian Manifolds ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields

scholarly journals Compact Orbits of Smooth Killing Vector Fields on Riemannian Manifolds

2000 ◽  
Vol 30 (1) ◽  
pp. 315-323
Author(s):  
Miroslav Lovrić
Keyword(s):  
Riemannian Manifolds ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields

scholarly journals On Fε2-planar mappings with function ε of (pseudo-)Riemannian manifolds

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2683-2689 ◽  
Author(s):  
Hana Chudá ◽  
Nadezda Guseva ◽  
Patrik Peska
Keyword(s):  
Partial Differential Equations ◽  
Riemannian Manifolds ◽  
Initial Conditions ◽  
Riemannian Metrics ◽  
Cauchy Type ◽  
Zero Function ◽  
Projective Equivalence ◽  
Type Form ◽  
Planar Mapping ◽  
Special Case

In this paper we study special mappings between n-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced PQ?-projectivity of Riemannian metrics, with constant ? ? 0,1 + n. These mappings were studied later by Matveev and Rosemann and they found that for ? = 0 they are projective. These mappings could be generalized for case, when ? will be a function on manifold. We show that PQ?- projective equivalence with ? is a function corresponds to a special case of F-planar mapping, studied by Mikes and Sinyukov (1983) with F = Q. Moreover, the tensor P is derived from the tensor Q and non-zero function ?. We assume that studied mappings will be also F2-planar (Mikes 1994). This is the reason, why we suggest to rename PQ? mapping as F?2. For these mappings we find the fundamental partial differential equations in closed linear Cauchy type form and we obtain new results for initial conditions.

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