arXiv subjects

Sourav Nayak

Publications and source records attributed to Sourav Nayak.

3 recordsLinked to original sources

arXiv2026

Characterization of Sasakian Manifolds by Curvature Conditions

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.

math.DG↗

arXiv2026

Characterizations of weak almost ${\mathcal S}$-manifolds with curvature properties

Weak metric structures, introduced by Rovenski and Wolak in 2022, extend Yano's $f$-structure and almost contact metric structure. In this paper, we investigate curvature phenomena of weak almost ${\cal S}$-manifolds (w.a.$\,\cal S$-manifolds) focusing on the $f$-$(κ,μ)$-nullity condition and its special case $R_{X,Y}\,ξ=0$. We establish several results that generalize known rigidity theorems for almost ${\cal S}$-manifolds. First, using the partial Ricci flow, we obtain dynamical characterizations of $\cal S$-manifolds: starting from a w.a.$\,\cal S$-structure satisfying the curvature condition of $\cal S$-manifolds or the $f$-$(1,μ)$-nullity condition, the flow evolves the structure exponentially fast toward an $\cal S$-structure. This extends results of Cappelletti Montano and Di Terlizzi to the weak metric setting. Next, we identify conditions under which a w.a.$\,{\cal S}$-manifold admits a bi-Legendrian structure with totally geodesic foliations. Finally, for w.a.$\,\cal S$-manifolds with $κ=μ=0$, we prove a splitting theorem in which one factor is flat, generalizing classical results for almost $\cal S$-geometry. These findings have consequences for the theory of Sasakian and $\cal S$- manifolds, the geometry of bi-Legendrian structures, and the behavior of weak metric contact manifolds under curvature constraints.

math.DG↗

arXiv2026

On the splitting of weak nearly ${\cal C}$-manifolds

The interest of mathematicians in metric $f$-manifolds, in particular, almost contact metric manifolds, is motivated by the study of the geometry and dynamics of contact foliations, as well as their applications in physics. Weak metric $f$-manifolds, defined by V. Rovenski and R. Wolak (2022), open a new perspective on classical theory of $f$-manifolds and discover new applications. In this paper, we study manifolds of this type, called weak nearly ${\cal C}$-manifolds, which generalize almost ${\cal C}$-manifolds. We find conditions under which a $(2n+s)$-dimensional weak nearly ${\cal C}$-manifold becomes locally a Riemannian product, and characterize $(4+s)$-dimensional weak nearly ${\cal C}$-manifolds. The consequences of these theorems present new results for nearly ${\cal C}$-manifolds.

math.DG↗