The paper studies para-Sasaki-like manifolds with a new metric connection.
problem Investigating new geometric structures on para-Sasaki-like manifolds.
method Deriving relations between connections, analyzing curvature tensors, studying solitons, constructing examples.
result Derived relations and properties of para-Sasaki-like manifolds with the generalized symmetric metric connection.
New Einstein metrics found from para-Sasaki-like Riemannian manifolds.
problem Finding new Einstein metrics in Riemannian geometry.
method Cone construction and hyperbolic extension of paracontact paracomplex Riemannian manifolds.
result New complete Einstein para-Sasaki-like Riemannian manifolds with negative scalar curvature.
A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian ma…
Yamabe solitons defined on specific Sasaki-like manifolds.
problem Defining Yamabe solitons on Sasaki-like almost contact B-metric manifolds.
method Contact conformal transformation of manifold components to define Yamabe solitons.
result Explicit 5-dimensional Lie group example of a Yamabe soliton.
Study of para-Ricci-like solitons on specific Riemannian manifolds.
problem Characterizing para-Ricci-like solitons on para-Sasaki-like Riemannian Π-manifolds. method Introduced and studied para-Ricci-like solitons with arbitrary potential. Proved properties of Ricci tensor and scalar curvatures.
result Ricci tensor is a constant multiple of the vertical component of both metrics, leading to equal and constant scalar curvatures.
Gradient almost para-Ricci-like solitons have constant coefficients and scalar curvatures.
problem Characterizing gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian Π-manifolds. method Proving constant coefficients and scalar curvatures through analysis of soliton properties.
result Constant coefficients and scalar curvatures for gradient almost para-Ricci-like solitons.
Study on Ricci-like solitons and gradient solitons on specific manifolds.
problem Characterizing solitons on Sasaki-like almost contact B-metric manifolds.
method Introduced and studied Ricci-like solitons with arbitrary potential and gradient solitons. Proved properties of the Ricci tensor and soliton coefficients.
result Gradient almost Ricci-like solitons have constant soliton coefficients.
Study para-Ricci-like solitons on special Riemannian manifolds, proving geometric properties and providing an example.
problem Characterize para-Ricci-like solitons on para-Sasaki-like Riemannian Π-manifolds. method Analyzed different cases of potential vectors and proved geometric properties of constructed objects.
result Obtained results for a parallel symmetric second-order covariant tensor and provided an explicit example.
The study examines null curves in specific geometric manifolds and their properties.
problem Characterizing null curves in Sasaki-like almost contact B-metric manifolds.
method Expressed Frenet frames and curvatures, proved curvature constancy conditions, and found necessary conditions for generalized helices and null cubic.
result Curvatures of specific null curves are constant if a function on the manifold is constant.
New solitons defined for Sasaki-like almost contact complex Riemannian manifolds.
problem Characterizing new solitons in Sasaki-like almost contact complex Riemannian manifolds.
method Defined β-Ricci-Bourguignon-like almost solitons with special potential. result Characterized geometrically and constructed examples of new solitons.
Study on Ricci-like solitons on specific geometric manifolds, finding properties and conditions.
problem Characterizing Ricci-like solitons on Sasaki-like almost contact B-metric manifolds.
method Analyzing cases with specific potential fields and studying curvature conditions.
result Found conditions for the potential to have constant length and manifold to be η-Einstein. Study of Yamabe solitons on specific geometric manifolds.
problem Characterizing Yamabe solitons on almost contact complex Riemannian manifolds.
method Investigation of two cases: Sasaki-like and torse-forming potentials.
result Explicit examples and theoretical properties confirmed in 3D.
Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-…
The object of study in the present dissertation are some topics in differential geometry of smooth manifolds with additional tensor structures and metrics of Norden type. There are considered four cases depending on the dimension of the manifold: 2n, 2n + 1, 4n and 4n + 3. The studied tensor structures, which are count…