arXiv subjects
Publications and source records attributed to Chandan Kumar Mondal.
As a generalization of geodesic function, in the present paper, we introduce the notion of geodesic $φ$-convex function and deduce some basic properties of $φ$-convex function and geodesic $φ$-convex function. We also introduce the concept of geodesic $φ$-convex set and $φ$-epigraph and investigate a characterization of geodesic $φ$-convex functions in terms of their $φ$-epigraphs.
Generalizing the notion of local $ϕ$-symmetry of Takahashi, in the present paper, we introduce the notion of local $ϕ$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $ϕ$-semisymmetry of a Sasakian manifold and obtain its characterization. It is shown that the local $ϕ$-semisymmetry, local projective $ϕ$-semisymmetry and local concircular $ϕ$-semisymmetry are equivalent. It is also shown that local conformal $ϕ$-semisymmetry and local conharmonical $ϕ$-semisymmetry are equivalent.
It is well known that among all closed bounded curves in the plane with the given perimeter, the circle encloses the maximum area. There are many proofs in the literature. In this article we have given a new proof using some ideas of Demar.