Gap theorems for compact almost Ricci-harmonic solitons

2019 ◽  
Vol 30 (08) ◽  
pp. 1950040 ◽  
Author(s):  
Abimbola Abolarinwa
Keyword(s):  
Einstein Metrics ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Compact Domain ◽  
Necessary And Sufficient ◽  
Gap Theorems

Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and sufficient conditions for a gradient shrinking almost Ricci-harmonic soliton on a compact domain to be almost harmonic-Einstein.

Gap theorems for compact gradient Sasaki–Ricci solitons

2015 ◽  
Vol 26 (04) ◽  
pp. 1540009
Author(s):  
Homare Tadano
Keyword(s):  
Ricci Curvature ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Necessary And Sufficient ◽  
Gap Theorems

In this paper, by using estimates for the transverse Ricci curvature in terms of the Sasaki–Futaki invariant, we shall give some gap theorems for compact gradient Sasaki–Ricci solitons by showing some necessary and sufficient conditions for the solitons to be Sasaki–Einstein. Our results may be regarded as a Sasaki geometry version of recent works by Li and Fernández-López and García-Río.

Hypersurfaces of Euclidean Space as Gradient Ricci Solitons

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Hana Al-Sodais ◽  
Haila Alodan ◽  
Sharief Deshmukh
Keyword(s):  
Euclidean Space ◽  
Sufficient Conditions ◽  
Ricci Soliton ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Gradient Ricci Soliton ◽  
Gradient Ricci Solitons ◽  
Necessary And Sufficient

Abstract In this paper we obtain some necessary and sufficient conditions for a hypersurface of a Euclidean space to be a gradient Ricci soliton. We also study the geometry of a special type of compact Ricci solitons isometrically immersed into a Euclidean space.

scholarly journals Curvature properties of almost Ricci-like solitons with torse-forming vertical potential on almost contact b-metric manifolds

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2679-2691
Author(s):  
Mancho Manev
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Einstein Manifold ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Contact Distribution ◽  
Necessary And Sufficient

A generalization of ?-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein like manifold, a generalization of an ?-Einstein manifold with respect to both B-metrics and functions as coefficients. Necessary and sufficient conditions are found for a number of properties of the curvature tensor and its Ricci tensor of the studied manifolds. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.

scholarly journals Gradient Ricci solitons on multiply warped product manifolds

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4221-4228
Author(s):  
Fatma Karaca ◽  
Cıhan Özgür
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Gradient Ricci Solitons ◽  
Necessary And Sufficient

We consider gradient Ricci solitons on multiply warped product manifolds. We find the necessary and sufficient conditions for multiply warped product manifolds to be gradient Ricci solitons.

On conformally related spherically symmetric Finsler metrics

2016 ◽  
Vol 13 (10) ◽  
pp. 1650118 ◽  
Author(s):  
Maryam Maleki ◽  
Nasrin Sadeghzadeh ◽  
Tahereh Rajabi
Keyword(s):  
Einstein Metrics ◽  
Finsler Geometry ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Conformal Transformations ◽  
Conformal Change ◽  
Projective Invariant ◽  
Necessary And Sufficient

In this paper, we study the projective invariant quantities in Finsler geometry which remain invariant under the conformal change of metrics. In particular, we obtain the necessary and sufficient conditions of a given Douglas and Weyl and generalized Douglas–Weyl (GDW) metric to be invariant under the conformal transformations. Finally, we introduce some explicit examples of these metrics. Also, some of these [Formula: see text]-conformal transformations of Einstein metrics are considered.

scholarly journals Invariant submanifolds of generalized Sasakian-space-forms

2018 ◽  
Vol 15 (09) ◽  
pp. 1850149 ◽  
Author(s):  
Shyamal Kumar Hui ◽  
Siraj Uddin ◽  
ALi H. Alkhaldi ◽  
Pradip Mandal
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Space Forms ◽  
Totally Geodesic ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Invariant Submanifolds ◽  
Levi Civita Connection ◽  
Necessary And Sufficient

This paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide an example of such submanifolds and obtain many new results including the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.

SOME GAP THEOREMS FOR GRADIENT RICCI SOLITONS

2012 ◽  
Vol 23 (07) ◽  
pp. 1250072 ◽  
Author(s):  
MANUEL FERNÁNDEZ-LÓPEZ ◽  
EDUARDO GARCÍA-RÍO
Keyword(s):  
Lower Bounds ◽  
Ricci Tensor ◽  
Sufficient Conditions ◽  
Ricci Soliton ◽  
Upper And Lower Bounds ◽  
Ricci Solitons ◽  
Gradient Ricci Soliton ◽  
Gradient Ricci Solitons ◽  
Necessary And Sufficient ◽  
Gap Theorems

Necessary and sufficient conditions for a gradient Ricci soliton to be Einstein are given, showing that they can be expressed in terms of upper and lower bounds on the behavior of the Ricci tensor when evaluated on the gradient of the potential function of the soliton.

scholarly journals Curvature Properties of Almost Ricci-Like Solitons with Torse-Forming Vertical Potential on Almost Contact B-Metric Manifolds

2021 ◽  
Author(s):  
MANCHO MANEV
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Einstein Manifold ◽  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Contact Distribution ◽  
Necessary And Sufficient

A generalization of $\eta$-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein-like manifold, a generalization of an $\eta$-Einstein manifold with respect to both B-metrics and functions as coefficients. Necessary and sufficient conditions are found for a number of properties of the curvature tensor and its Ricci tensor of the studied manifolds. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.

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

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

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.

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