1,720,964 research outputs found
GENERALIZED η-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS ASSOCIATED TO THE SCHOUTEN-VAN KAMPEN CONNECTION
Full text linkIn this paper, we study generalized η-Ricci solitons with respect to the Schouten-van Kampen connection on trans-Sasakian manifolds. We give an example of generalized η-Ricci solitons on a trans-Sasakian manifold with respect to the Schouten-van Kampen connection to prove our results
SOME RESULTS ON -ALMOST SOLITONS ON ALMOST CO-K\"{A}HLER MANIFOLDS
No full textThe object of the present paper is to study -almost Yamabe solitons and -almost Ricci solitons on almost co-K\"{a}hler manifolds. In this paper, we prove that if an almost co-K\"{a}hler manifold with the Reeb vector field admits a -almost Yamabe solitons with the potential vector field or , where is a smooth function then manifold is -almost co-K\"{a}hler manifold or the soliton is trivial, respectively. Also, we show if a closed -almost co-K\"{a}hler manifold with and admits a -almost Yamabe soliton then the soliton is trivial and expanding. Then we study an almost co-K\"{a}hler manifold admits a -almost Yamabe soliton or -almost Ricci soliton with as the potential vector field, is a special geometric vector field
CERTAIN RESULTS ON -RICCI SOLITIONS AND ALMOST -RICCI SOLITONS
No full textWe prove that if an -Einstein para-Kenmotsu manifold admits a -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a -Ricci soliton is Einstein if its potential vector field is infinitesimal paracontact transformation or collinear with the Reeb vector field. Further, we prove that if a para-Kenmotsu manifold admits a gradient almost -Ricci soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits -Ricci soliton and satisfy our results. We also have studied -Ricci soliton in 3-dimensional normal almost paracontact metric manifolds and we show that if in a 3-dimensional normal almost paracontact metric manifold with = constant, the metric is -Ricci soliton, where potential vector field is collinear with the characteristic vector field , then the manifold is -Einstein manifold
THE LOWER BOUNDS FOR THE FIRST EIGENVALUE OF THE BIHARMONIC AND p-BIHARMONIC OPERATORS ON FINSLER MANIFOLDS
Full text linkIn this paper, we are going to estimate the lower bounds for the first eigenvalues of the buckling problem and clamped plate problem by considering a positive lower bound for the weighted Ricci curvature. Also, we extended the results for the p-biharmonic operator and we prove a Lichnerowicz-Obata-Cheng type estimate for the biharmonic operators
Some geometric estimates of the first eigenvalue of quasilinear and -Laplace operators
Full text linkIn this paper, we use a particular smooth function on a bounded domain of a Riemannian manifold to estimate the lower bound of the first eigenvalue for quasilinear operator . In this way, we also present a lower bound for the first eigenvalue of the -Laplacian on compact manifolds
Harmonic-hyperbolic geometric flow
No full textIn this article we study a coupled system for hyperbolic geometric
flow on a closed manifold M, with a harmonic flow map from M to
some closed target manifold N.
Then we show that this flow has a unique solution for a short-time.
After that, we find evolution equations for Riemannian curvature tensor,
Ricci curvature tensor, and scalar curvature of M under this flow.
In the final section we give some examples of this flow on closed manifolds
FUNDAMENTAL TONE ESTIMATES ON FINSLER MANIFOLDS
Full text linkWe study the fundamental tone of Laplacian operators on Finsler manifold evolved by a special function , and we give some geometric estimates of the first eigenvalue of p-laplace and (p,q)-Laplace operators depend on this function for simply connected manifolds, a class of warped product manifolds, and a class of Finsler submersions. Under a similar setting, we also study these results on a quasi-linear operator
RICCI SOLITONS AND RICCI BI-CONFORMAL VECTOR FIELDS ON THE MODEL SPACE
Full text linkIn this paper, we classify the Ricci solitons and the Ricci bi-conformal vector fields on model space . We also show which of them are gradient vector fields and which one of those are Killing vector fields
Generalized parabolic frequency on compact manifolds
Full text linkIn this paper, we first prove monotonicity of a generalized para bolic
frequency on weighted closed Riemannian manifolds for some linear heat
equation. Secondly, a certain generalized parabolic frequency functional is
defined with respect to the solutions of a nonlinear weighted p-heat-type
equation on manifolds, and its monotonicity is proved. Notably, the
monotonicities are derived with no assumption on both the curvature and the
potential function. Further consequences of these monotonicity formulas from
which we can get backward uniqueness are discussedComment: 14 page
Parabolic frequency monotonicity on the conformal Ricci flow
Full text linkThis paper is devoted to the investigation of the monotonicity of parabolic
frequency functional under conformal Ricci flow defined on a closed Riemannian
manifold of constant scalar curvature and dimension not less than 3. Parabolic
frequency functional for solutions of certain linear heat equation coupled with
conformal pressure is defined and its monotonicity under the conformal Ricci
flow is proved by applying Bakry-Emery Ricci curvature bounds. Some
consequences of the monotonicity are also presented.Comment: 18 page
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