On the reversible geodesics of a Finsler space endowed with a special deformed (α,β)(\alpha, \beta)-metric

The scope of this paper is twofold. On the one hand, we will investigate the reversible geodesics of a Finsler space endowed with the deformed newly introduced $(\alpha, \beta)$-metric\begin{equation}F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta\end{equation}where $\epsilon$ is a real parameter with $|\epsilon|<2\sqrt{a+1}$ and $a\in \left(\frac{1}{4},+\infty\right)$; and on the other hand, we will investigate the T-tensor for this metric

Bézier type surfaces

In this paper with the help of the fundamental polynomials, from general operators, we construct Bézier-type and GBS Bézier-type surfaces, which correspond to the given control points

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics

Null Homology Groups and Stable Currents in Warped Product Submanifolds of Euclidean Spaces

In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups are vanishing, and M3 is homotopic to the Euclidean sphere S3 under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature, and the Hessian tensor. The results in this paper can be considered an extension of Xin’s work in the framework of a compact warped product submanifold, when the base manifold is minimal in ambient manifolds

On the Topology of Warped Product Pointwise Semi-Slant Submanifolds with Positive Curvature

In this paper, we obtain some topological characterizations for the warping function of a warped product pointwise semi-slant submanifold of the form &Omega;n=NTl&times;fN&#981;k in a complex projective space CP2m(4). Additionally, we will find certain restrictions on the warping function f, Dirichlet energy function E(f), and first non-zero eigenvalue &lambda;1 to prove that stable l-currents do not exist and also that the homology groups have vanished in &Omega;n. As an application of the non-existence of the stable currents in &Omega;n, we show that the fundamental group &pi;1(&Omega;n) is trivial and &Omega;n is simply connected under the same extrinsic conditions. Further, some similar conclusions are provided for CR-warped product submanifolds