Dhriti Sundar Patra — Neckpinch

Characterization of Sasakian Manifolds by Curvature Conditions

Mon, 05 Oct 2026 00:00:00 GMT

Sourav Nayak, Vladimir Rovenski, Dhriti Sundar Patra — 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.

Characterizations of Almost Ricci Bourguignon Solitons

Fri, 19 Dec 2025 00:00:00 GMT

Mohammad Aqib, Hemangi Madhusudan Shah, Dhriti Sundar Patra — In this paper, we revisit the study of almost Ricci-Bourguignon solitons by clarifying their position in the broader context of Einstein-type metrics. Motivated by known rigidity results for compact almost Ricci solitons, we aim to identify conditions under which a compact almost RB-soliton is trivial or exhibits special geometric properties. We compare our results with classical theorems of Barros and Ribeiro, and explain explicitly how our work extends or complements these earlier findings.

Characterizations of weak almost {𝓢-manifolds with curvature properties

Tue, 12 Aug 2025 00:00:00 GMT

Sourav Nayak, Dhriti Sundar Patra, Vladimir Rovenski — 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.