International Journal of Maps in Mathematics

Translation framed surfaces generated by non-null framed curves in Minkowski 3-space

2024-02-09T14:28:10+00:00

In this paper, first we obtain the conditions for the existence and uniqueness of non-null framed curves as well as non-null framed surfaces in Minkowski $3$-space. Further, we study the timelike and spacelike translation framed surfaces generated by non-null framed curves and obtain the basic invariants of such surfaces in $\E^3_1$. We also find the curvatures of timelike and spacelike translation framed surfaces generated by non-null framed curves. Finally, we classify the translation framed surfaces generated by non-null framed curves lying in mutually perpendicular coordinate planes of $\E^3_1$ with $\K_K \equiv 0$ and $\K_H \equiv 0$.

Generalized solitonic characteristics in trans para Sasakian manifolds

2024-01-18T11:04:34+00:00

In the current research, we quantify the almost generalized Ricci soliton on the trans-para-Sasakian manifold as well as the gradient almost generalized Ricci soliton. Trans-para Sasakian manifolds that meet certain criteria are also required to be Einstein manifolds. It is demonstrated that the almost generalized Ricci soliton equation is also satisfied by some manifolds, notably $\alpha$-para-Sasakian and $\beta$-para -Kenmotsu manifolds. The fact that a compact trans-para-Sasakian admits both a convex Einstein potential with non-negative scalar curvature and a gradient almost generalized Ricci soliton with Hodge-de Rham potential has also been covered.