Characterization of Sasakian Manifolds by Curvature Conditions
Abstract
Sasakian manifolds, a subclass of contact metric manifolds, play a central role in modern differential geometry and mathematical physics, where they arise naturally in geometric mechanics, CR geometry, and supersymmetric field theories. The weak contact metric (w.c.m.) structure generalizes the contact metric structure and provides a broader framework for studying contact geometry and its applications. A fundamental problem is to understand how curvature conditions constrain the underlying contact metric structure and, in particular, how they distinguish Sasakian geometry from its weaker variants. Using the partial Ricci flow, we characterize Sasakian structure (among w.c.m. manifolds) under the (κ,μ)-nullity condition related to curvature. For κ<1 we find conditions under which a w.c.m. manifold admits a bi-Legendrian structure, and for κ=μ=0 establish splitting and classification results.
Related
- Curvature characterization of Hermitian manifolds with Bismut parallel torsion
- Rigidity of Einstein Manifolds under Two Eigenvalue Conditions on the Curvature Operator of the Second Kind
- Hitchin sections on $3$-dimensional Sasakian manifolds
- Three-dimensional noncompact trans-Sasakian η-Einstein manifolds
- Laplace and Dolbeault operators on Sasakian manifolds
BibTeX
@misc{nayak2026characterization,
title = {{Characterization of Sasakian Manifolds by Curvature Conditions}},
author = {Sourav Nayak and Vladimir Rovenski and Dhriti Sundar Patra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06463},
eprint = {2610.06463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06463},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Characterization of Sasakian Manifolds by Curvature Conditions
AU - Sourav Nayak
AU - Vladimir Rovenski
AU - Dhriti Sundar Patra
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.06463
UR - https://arxiv.org/abs/2610.06463
AB - Sasakian manifolds, a subclass of contact metric manifolds, play a central role in modern differential geometry and mathematical physics, where they arise naturally in geometric mechanics, CR geometry, and supersymmetric field theories. The weak contact metric (w.c.m.) structure generalizes the contact metric structure and provides a broader framework for studying contact geometry and its applications. A fundamental problem is to understand how curvature conditions constrain the underlying contact metric structure and, in particular, how they distinguish Sasakian geometry from its weaker variants. Using the partial Ricci flow, we characterize Sasakian structure (among w.c.m. manifolds) under the (κ,μ)-nullity condition related to curvature. For κ<1 we find conditions under which a w.c.m. manifold admits a bi-Legendrian structure, and for κ=μ=0 establish splitting and classification results.
ER -