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

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 Ricci iterations on Kähler classes

2009 ◽  
Vol 8 (4) ◽  
pp. 743-768 ◽  
Author(s):  
Julien Keller
Keyword(s):  
Iterative Procedure ◽  
Einstein Metrics ◽  
Einstein Manifold ◽  
Periodic Points ◽  
Dynamical Behaviour ◽  
Iteration Scheme ◽  
Fano Manifold ◽  
Ricci Operator ◽  
Finite Dimensional ◽  
Kähler Einstein Metrics

AbstractIn this paper we consider the dynamical system involved by the Ricci operator on the space of Kähler metrics of a Fano manifold. Nadel has defined an iteration scheme given by the Ricci operator and asked whether it has some non-trivial periodic points. First, we prove that no such periodic points can exist. We define the inverse of the Ricci operator and consider the dynamical behaviour of its iterates for a Fano Kähler–Einstein manifold. Then we define a finite-dimensional procedure to give an approximation of Kähler–Einstein metrics using this iterative procedure and apply it on ℂℙ2 blown up in three points.

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