Trans-Sasakian space forms
Abstract
In this paper, we derive an explicit expression for the Riemann--Christoffel curvature tensor of a trans-Sasakian manifold with pointwise constant φ-sectional curvature and introduce the notion of trans-Sasakian space forms. As consequences, we obtain explicit formulas for the Ricci tensor and the scalar curvature. We further prove that every $3$-dimensional trans-Sasakian manifold necessarily has pointwise constant φ-sectional curvature. In addition, we investigate statistical structures on trans-Sasakian manifolds and introduce the notion of trans-Sasakian statistical space forms. We then establish a classification of such statistical structures. Our results show that every trans-Sasakian statistical space form of dimension greater than $3$ is necessarily almost-trivial. In the $3$-dimensional case, we establish a rigidity theorem for trans-Sasakian statistical space forms and provide explicit examples showing the existence of non-trivial $3$-dimensional trans-Sasakian statistical space forms
Related
- Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
- Hypersurfaces with constant sectional curvature of a product of two space forms
- Isospectral and not strongly isospectral spherical space forms with non-cyclic fundamental group
- Isoparametric Submanifolds in Products of Space Forms
- Biharmonic Lagrangian H-umbilical submanifolds in complex space forms
BibTeX
@misc{prachi2026transsasakian,
title = {{Trans-Sasakian space forms}},
author = {Prachi and Mukut Mani Tripathi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07680},
eprint = {2611.07680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07680},
}
RIS
TY - UNPB
TI - Trans-Sasakian space forms
AU - Prachi
AU - Mukut Mani Tripathi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07680
UR - https://arxiv.org/abs/2611.07680
AB - In this paper, we derive an explicit expression for the Riemann--Christoffel curvature tensor of a trans-Sasakian manifold with pointwise constant φ-sectional curvature and introduce the notion of trans-Sasakian space forms. As consequences, we obtain explicit formulas for the Ricci tensor and the scalar curvature. We further prove that every $3$-dimensional trans-Sasakian manifold necessarily has pointwise constant φ-sectional curvature. In addition, we investigate statistical structures on trans-Sasakian manifolds and introduce the notion of trans-Sasakian statistical space forms. We then establish a classification of such statistical structures. Our results show that every trans-Sasakian statistical space form of dimension greater than $3$ is necessarily almost-trivial. In the $3$-dimensional case, we establish a rigidity theorem for trans-Sasakian statistical space forms and provide explicit examples showing the existence of non-trivial $3$-dimensional trans-Sasakian statistical space forms
ER -