The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.
problem Classifying h-almost Ricci-Yamabe solitons in paracontact geometry.
method Characterization and classification of para-Kenmotsu, para-Sasakian, and para-cosymplectic manifolds.
result Characterizations and classifications of various paracontact manifolds.
Study on η-Ricci-Yamabe solitons on Riemannian submersions.
problem Characterizing η-Ricci-Yamabe solitons on Riemannian submersions. method Analyzing conditions for η-Ricci-Yamabe solitons on submersions and deriving Laplacian equations. result Classification of fiber and target manifolds as η-Ricci-Yamabe solitons under various conditions. Characterizes ∗-k-Ricci-Yamabe solitons on Kenmotsu manifolds.
problem Understanding ∗-k-Ricci-Yamabe solitons on Kenmotsu manifolds. method Analyzes the geometry of ∗-k-Ricci-Yamabe solitons and gradient solitons on Kenmotsu manifolds. result Characterizes the nature of ∗-k-Ricci-Yamabe solitons and gradient solitons. The paper characterizes solitons and estimates scalar curvature.
problem Characterizing and estimating scalar curvature of generalized Ricci-Yamabe solitons.
method Characterization and estimation of scalar curvature through soliton properties.
result Conditions for scalar curvature to be constant and estimation of Ricci curvature.
The (α,β)-Ricci-Yamabe flow exists on closed manifolds.
problem Existence of solutions to the (α,β)-Ricci-Yamabe flow. method Showed short time existence and established long time existence theorems.
result Existence of smooth solutions to the (α,β)-Ricci-Yamabe flow on closed manifolds. The paper characterizes specific almost Kenmotsu manifolds with Ricci-Yamabe solitons.
problem Characterizing almost Kenmotsu manifolds with Ricci-Yamabe solitons.
method Analyzing curvature properties and potential vector fields.
result Locally isometric structures of specific almost Kenmotsu manifolds.
Study of Ricci-Yamabe solitons on Walker 3-manifolds.
problem Characterizing Ricci-Yamabe solitons on Walker 3-manifolds.
method Using Hodge decomposition of De-Rham, the soliton field is found from the potential function.
result Classification of all Ricci-Yamabe and gradient Ricci-Yamabe solitons in a Walker 3-manifold.
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
The study classifies contact metric manifolds based on Ricci-Yamabe solitons.
problem Classifying contact metric manifolds based on Ricci-Yamabe solitons.
method Analyzing specific types of solitons in contact metric manifolds.
result Contact metric manifolds are classified based on the properties of Ricci-Yamabe solitons.
The study examines almost Ricci-Yamabe solitons on almost Kenmotsu manifolds and their properties.
problem Characterizing almost Ricci-Yamabe solitons on almost Kenmotsu manifolds.
method Analyzing the conditions for almost Ricci-Yamabe solitons to be η-Einstein and proving local isometry for certain manifolds.
result Properties of almost Ricci-Yamabe solitons on (2n+1)-dimensional (κ,μ)′-AKMs. The paper studies ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds.
problem Exploring ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. method Analyzing curvature properties and developing soliton characteristics with respect to quarter-symmetric metric connection.
result Characteristics and nature of ∗-η-Ricci-Yamabe solitons on α-Cosymplectic manifolds. Study on Ricci-Yamabe solitons on Walker manifolds.
problem Characterizing Walker manifolds for Ricci-Yamabe solitons.
method Explicit calculation of Ricci tensor, scalar curvature, and Hessian Perelman potential; solving partial differential equations.
result Identifying constraints on functions and vector field for soliton existence.
The study introduces a new soliton concept to classify Sasakian 3-manifolds.
problem Classifying Sasakian 3-manifolds under specific conditions.
method Introducing and studying ∗-Ricci-Yamabe solitons on contact metric manifolds. result Sasakian 3-manifolds admitting ∗-Ricci-Yamabe solitons are ∗-Ricci flat, positive Sasakian, and have Fano transverse geometry. The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow g(t). The considered flow in covariant symmetric 2-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of g(t). Due to the signs of…
The paper explores properties of conformal vector fields on almost Kenmotsu manifolds.
problem Characterizing properties of conformal vector fields on almost Kenmotsu manifolds.
method Analyzing conformal vector fields as Reeb vector fields and pointwise collinear, proving manifold properties and existence of warped products.
result Conformal vector fields on almost Kenmotsu manifolds lead to specific manifold structures and properties.
Characterizes and examines gradient solitons on doubly warped product manifolds.
problem Understanding gradient solitons on specific manifold structures.
method Characterizations and examinations of various types of gradient solitons on doubly warped product manifolds.
result Effects of gradient solitons on factor manifolds and specific curvature properties of doubly warped products.
Second part of a study on heat equations on special manifolds, focusing on parametrix construction.
problem Analysis of heat-type equations on manifolds with fibered boundaries.
method Construction of parametrix for heat-type equations.
result Inference of existence and regularity of certain parabolic equations.
Hyperbolic solitons on trans-Sasakian space forms and their submanifolds
problem Characterizing hyperbolic solitons on trans-Sasakian space forms and their submanifolds
method Introducing hyperbolic ∗−Ricci solitons and hyperbolic Ricci-Yamabe solitons result Characterizing the nature of hyperbolic solitons on trans-Sasakian space forms and their submanifolds
The paper examines geometric properties of a specific black hole spacetime.
problem Curvature properties of a Hayward black hole spacetime.
method Analyzes the curvature properties of Hayward black hole spacetime using Einstein field equations.
result The Hayward black hole spacetime is an Einstein manifold and exhibits various types of pseudosymmetry.