scholarly journals Sasakian metric as a Ricci soliton and related results

2014 ◽  
Vol 75 ◽  
pp. 1-6 ◽  
Author(s):  
Amalendu Ghosh ◽  
Ramesh Sharma
Keyword(s):  
Ricci Soliton ◽  
Sasakian Metric

SASAKIAN 3-MANIFOLD AS A RICCI SOLITON REPRESENTS THE HEISENBERG GROUP

2011 ◽  
Vol 08 (01) ◽  
pp. 149-154 ◽  
Author(s):  
RAMESH SHARMA ◽  
AMALENDU GHOSH
Keyword(s):  
Vector Field ◽  
Heisenberg Group ◽  
Contact Structure ◽  
Ricci Soliton ◽  
Potential Vector ◽  
3 Dimensional ◽  
Sasakian Metric ◽  
Potential Vector Field

We show that, if a 3-dimensional Sasakian metric is a non-trivial Ricci soliton, then it is expanding and homothetic to the standard Sasakian metric on the Heisenberg group nil3. We have also discussed properties of the Ricci soliton potential vector field that relate to the underlying contact structure.

∗-Ricci Soliton within the frame-work of Sasakian and (κ,μ)-contact manifold

2018 ◽  
Vol 15 (07) ◽  
pp. 1850120 ◽  
Author(s):  
Amalendu Ghosh ◽  
Dhriti Sundar Patra
Keyword(s):  
Unit Sphere ◽  
Contact Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Contact Manifolds ◽  
Gradient Ricci Soliton ◽  
Frame Work ◽  
Sasakian Metric

We prove that if a Sasakian metric is a ∗-Ricci Soliton, then it is either positive Sasakian, or null-Sasakian. Next, we prove that if a complete Sasakian metric is an almost gradient ∗-Ricci Soliton, then it is positive-Sasakian and isometric to a unit sphere [Formula: see text]. Finally, we classify nontrivial ∗-Ricci Solitons on non-Sasakian [Formula: see text]-contact manifolds.

Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri ◽  
Cornelia-Livia Bejan
Keyword(s):  
Vector Fields ◽  
Ricci Soliton ◽  
Conformal Vector ◽  
Conformal Vector Fields

scholarly journals Concurrent Vector Fields on Lightlike Hypersurfaces

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 59
Author(s):  
Erol Kılıç ◽  
Mehmet Gülbahar ◽  
Ecem Kavuk
Keyword(s):  
Vector Fields ◽  
Ricci Soliton ◽  
Lorentzian Manifold ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Lightlike Hypersurfaces

Concurrent vector fields lying on lightlike hypersurfaces of a Lorentzian manifold are investigated. Obtained results dealing with concurrent vector fields are discussed for totally umbilical lightlike hypersurfaces and totally geodesic lightlike hypersurfaces. Furthermore, Ricci soliton lightlike hypersurfaces admitting concurrent vector fields are studied and some characterizations for this frame of hypersurfaces are obtained.

Twisted Sasakian Metric on the Tangent Bundle and Harmonicity

2021 ◽  
Vol 62 ◽  
pp. 53-66
Author(s):  
Fethi Latti ◽  
◽  
Hichem Elhendi ◽  
Lakehal Belarbi
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Harmonic Vector ◽  
New Class ◽  
Necessary And Sufficient ◽  
Sasakian Metric ◽  
Harmonic Vector Fields

In the present paper, we introduce a new class of natural metrics on the tangent bundle $TM$ of the Riemannian manifold $(M,g)$ denoted by $G^{f,h}$ which is named a twisted Sasakian metric. A necessary and sufficient conditions under which a vector field is harmonic with respect to the twisted Sasakian metric are established. Some examples of harmonic vector fields are presented as well.

scholarly journals ON THE MODIFIED FUTAKI INVARIANT OF COMPLETE INTERSECTIONS IN PROJECTIVE SPACES

2016 ◽  
Vol 222 (1) ◽  
pp. 186-209
Author(s):  
RYOSUKE TAKAHASHI
Keyword(s):  
Vector Field ◽  
Recent Work ◽  
Projective Spaces ◽  
Ricci Soliton ◽  
Complete Intersections ◽  
Necessary Condition ◽  
Ricci Solitons ◽  
Fano Varieties ◽  
Holomorphic Vector Field ◽  
Fano Manifold

Let $M$ be a Fano manifold. We call a Kähler metric ${\it\omega}\in c_{1}(M)$ a Kähler–Ricci soliton if it satisfies the equation $\text{Ric}({\it\omega})-{\it\omega}=L_{V}{\it\omega}$ for some holomorphic vector field $V$ on $M$. It is known that a necessary condition for the existence of Kähler–Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian and Zhu. In a recent work of Berman and Nyström, it was generalized for (possibly singular) Fano varieties, and the notion of algebrogeometric stability of the pair $(M,V)$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.

Unitary vector fields are Fermi–Walker transported along Rytov–Legendre curves

2015 ◽  
Vol 12 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Mircea Crasmareanu ◽  
Camelia Frigioiu
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Conformal Killing ◽  
Space Forms ◽  
Potential Vector ◽  
Legendre Curves ◽  
Complex Space Forms

Fix ξ a unitary vector field on a Riemannian manifold M and γ a non-geodesic Frenet curve on M satisfying the Rytov law of polarization optics. We prove in these conditions that γ is a Legendre curve for ξ if and only if the γ-Fermi–Walker covariant derivative of ξ vanishes. The cases when γ is circle or helix as well as ξ is (conformal) Killing vector filed or potential vector field of a Ricci soliton are analyzed and an example involving a three-dimensional warped metric is provided. We discuss also K-(para)contact, particularly (para)Sasakian, manifolds and hypersurfaces in complex space forms.

scholarly journals Toric extremal Kähler-Ricci solitons are Kähler-Einstein

2017 ◽  
Vol 4 (1) ◽  
pp. 179-182 ◽  
Author(s):  
Simone Calamai ◽  
David Petrecca
Keyword(s):  
General Problem ◽  
Short Note ◽  
Kähler Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Toric Manifolds ◽  
Kahler Manifold

Abstract In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

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