Self-dual manifolds with non-negative ricci operator

1991 ◽  
pp. 55-61 ◽  
Author(s):  
Paul Gauduchon
Keyword(s):  
Ricci Operator

Reeb flow symmetry on 3-dimensional almost paracosymplectic manifolds

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2355-2365
Author(s):  
Irem Küpeli
Keyword(s):  
Ricci Operator ◽  
3 Dimensional ◽  
Flow Symmetry

Mainly, we prove that the Ricci operator Q of an 3-dimensional almost paracosymplectic manifold M is invariant along the Reeb flow, that is M satisfies L?Q = 0 if and only if M is an almost paracosymplectic k-manifold with k ? -1.

scholarly journals The property of real hypersurfaces in 2-dimensional complex space form with Ricci operator

2014 ◽  
Vol 38 ◽  
pp. 920-923 ◽  
Author(s):  
Dong Ho LIM ◽  
Woon Ha SOHN ◽  
Seong-Soo AHN
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ricci Operator

Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres

1989 ◽  
Vol 108 (2-3) ◽  
pp. 211-217 ◽  
Author(s):  
Philippe Tondeur ◽  
Lieven Vanhecke
Keyword(s):  
Ricci Operator ◽  
Geodesic Spheres

scholarly journals Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 246
Author(s):  
Yan Zhao ◽  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Ricci Operator ◽  
Cosymplectic Manifold

Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.

scholarly journals Ricci operator in a Hopf real Hypersurfaces of complex space form

2020 ◽  
Vol 1597 ◽  
pp. 012049
Author(s):  
Uppara Manjulamma ◽  
H G Nagaraja ◽  
D L Kiran Kumar
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ricci Operator

CERTAIN RESULTS ON THREE-DIMENSIONAL CONTACT METRIC MANIFOLDS

2010 ◽  
Vol 03 (04) ◽  
pp. 577-591 ◽  
Author(s):  
Amalendu Ghosh
Keyword(s):  
Ricci Tensor ◽  
Three Dimensional ◽  
Tensor Fields ◽  
Contact Metric Manifold ◽  
Ricci Operator ◽  
3 Dimensional ◽  
Contact Metric Manifolds ◽  
Parallel Ricci Tensor

In this paper we study 3-dimensional contact metric manifolds satisfying certain conditions on the tensor fields *-Ricci tensorS*, h(= ½Lξφ), τ(= Lξg = 2hφ) and the Ricci operator Q. First, we prove that a 3-dimensional non-Sasakian contact metric manifold satisfies. [Formula: see text] (where ⊕X,Y,Z denotes the cyclic sum over X,Y,Z) if and only if M is a generalized (κ, μ)-space. Next, we prove that a 3-dimensional contact metric manifold with vanishing *-Ricci tensor is a generalized (κ, μ)-space. Finally, some results on 3-dimensional contact metric manifold with cyclic η-parallel h or cyclic η-parallel τ or η-parallel Ricci tensor are presented.

Unit tangent sphere bundles with the Reeb flow invariant Ricci operator

2017 ◽  
Vol 40 (1) ◽  
pp. 102-116
Author(s):  
Jong Taek Cho ◽  
Sun Hyang Chun
Keyword(s):  
Ricci Operator ◽  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles

scholarly journals Algebraic Ricci Solitons on Metric Lie Groups with Nondiagonalizable Ricci Operator

2017 ◽  
Vol 1 ◽  
Author(s):  
P.N. Klepikov ◽  
◽  
E.D. Rodionov ◽  
Keyword(s):  
Lie Groups ◽  
Ricci Solitons ◽  
Ricci Operator

The Abbena-Thurston Manifold as a Critical Point

1996 ◽  
Vol 39 (3) ◽  
pp. 352-359 ◽  
Author(s):  
Joon-Sik Park ◽  
Won Tae Oh
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Ricci Operator

AbstractThe Abbena-Thurston manifold (M,g) is a critical point of the functional where Q is the Ricci operator and R is the scalar curvature, and then the index of I(g) and also the index of — I(g) are positive at (M,g).

scholarly journals Mathematical Modeling in the Study of the Ricci Operator on Four-Dimensional Locally Homogeneous (Pseudo)Riemannian Manifolds with Isotropic Weyl Tensor

2020 ◽  
pp. 92-95
Author(s):  
S.V. Klepikova ◽  
T.P. Makhaeva
Keyword(s):  
Riemannian Manifolds ◽  
Weyl Tensor ◽  
Three Dimensional ◽  
Isotropy Subgroup ◽  
Ricci Operator ◽  
One Dimensional ◽  
3 Dimensional ◽  
Homogeneous Riemannian Manifolds ◽  
Locally Homogeneous ◽  
The One

It is known that a locally homogeneous manifold can be obtained from a locally conformally homogeneous (pseudo)Riemannian manifolds by a conformal deformation if the Weyl tensor (or the Schouten-Weyl tensor in the three-dimensional case) has a nonzero squared length. Thus, the problem arises of studying (pseudo)Riemannian locally homogeneous and locally conformally homogeneous manifolds, the Weyl tensor of which has zero squared length, and itself is not equal to zero (in this case, the Weyl tensor is called isotropic). One of the important aspects in the study of such manifolds is the study of the curvature operators on them, namely, the problem of restoring a (pseudo)Riemannian manifold from a given Ricci operator. The problem of the prescribed values of the Ricci operator on 3-dimensional locally homogeneous Riemannian manifolds has been solved by O. Kowalski and S. Nikcevic. Analogous results for the one-dimensional and sectional curvature operators were obtained by D.N. Oskorbin, E.D. Rodionov, and O.P Khromova. This paper is devoted to the description of an example of studying the problem of the prescribed Ricci operator for four-dimensional locally homogeneous (pseudo) Riemannian manifolds with a nontrivial isotropy subgroup and isotropic Weyl tensor.

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