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Dr. S. K. Srivastava

Central University of Himachal Pradesh School of Mathematics Computers and Information Science, Central University of Himachal Pradesh, Deen Dayal Upadhyaya Gorakhpur University

ORCID iD 0000-0001-5992-1902
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About

I am currently working as a Professor (Associate) at Central University of Himachal Pradesh, India. I have obtained PhD in Mathematics from DDU Gorakhpur University, Gorakhpur. I have carried out my research work on the Hypersurfaces of Sasakian Manifolds for the PhD and supervised by Prof. Dhruwa Narain.
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My primary area of research is Warped Geometry and its applications. Warped geometry is a foundational concept in differential geometry and theoretical physics, wherein the geometry of a space is modified by a smooth function—known as a warping function—that scales the metric of one part of the space relative to another. This framework is particularly significant in general relativity, cosmology, and string theory, where warped product manifolds are used to model spacetime configurations that vary across different dimensions.

Several key solutions to Einstein’s field equations, including the Friedmann models and Robertson–Walker spacetimes, are formulated using warped products. In string theory, warped product spaces such as $\mathbb{S}_1^n \times \mathbb{F}$ and $\mathbb{H}_1^n \times \mathbb{F}$—where $\mathbb{F}$ is a Calabi–Yau manifold and $\mathbb{S}_1^n$ (respectively $\mathbb{H}_1^n$) denotes de Sitter (respectively anti-de Sitter) space—play a crucial role in describing higher-dimensional spaces and brane-world scenarios.

Warped geometries also have profound implications in geometric analysis, especially in the study of partial differential equations on curved spaces. Furthermore, the theory of submanifolds, supported by the Nash embedding theorem, demonstrates that any warped product can be realized as a Riemannian submanifold of Euclidean space. This connection extends the relevance of warped geometry to diverse fields, including mathematical physics, mathematical biology, computer-aided design, and image processing.

Secondly, I aim to explore and advance the applications of warped geometry in mathematical biology, driven by my interest in modeling biological phenomena and complex systems using geometric frameworks and analysis.

Finally, I intend to focus on Vedic studies by fostering interdisciplinary collaborations with departments such as Sanskrit, Botany, Chemistry, and Physics. My objective is to integrate traditional knowledge with modern scientific approaches to contribute to and enrich the Indian Knowledge System (IKS).
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Employment

  • Central University of Himachal Pradesh School of Mathematics Computers and Information Science Associate Professor
    2025 - Present
  • Central University of Himachal Pradesh Assistant Professor
    2012 - 2025

Education

  • Deen Dayal Upadhyaya Gorakhpur University Ph.D.
    2003 - 2010

Projects & Funding

Projects & funding information is unavailable.

Publications (20)