Dr Pankaj Kumar received his PhD from Banaras Hindu University, Varanasi. The main area of his research is Differential Geometry. He has completed numerous courses/Training/workshops conducted by highly reputed organisations. Dr Pankaj interested in the study of Einstein warped product space and its applications in Mathematical Physics. There was an open problem asked by A. L. Besse that is, “Does there exists a compact Einstein warped product space with non-constant warping function?” Kim and Kim gave a partial answer to this open problem. However, they did not consider the problem for Compact Einstein multiply warped product. This is where Dr. Pankaj started their research. Dr. Pankaj also study the above-mentioned open problem for Einstein Poisson warped product space. Apart from these, Dr. Kumar also studied Killing forms (Killing 1-form and Killing 2-form) on Riemannian Poisson warped product space. He has several publications published in peer-reviewed journals.

Experience

• Teaching: 11 Months
• Research Experience: 05 years.

Education Qualification

• Doctor of Philosophy (Ph.D.) in Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India. (2017-2022).

Ph.D. Thesis title: Warped Product on some Riemannian Manifolds.

Supervisor: Dr. Buddhadev Pal.

• Post Graduation (Sc.) in Mathematics from Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India (2013-2015).

• Graduation (Sc.) in Mathematics and Physics from V. B. S. Purvanchal University Jaunpur (2009-2012).

Award & Recognition

• Awarder by CSIR-UGC NET (JRF-Mathematical Sciences) on 23^rd March, 2017.

Research Papers Published

• Buddhadev Pal and Pankaj Kumar, Compact Einstein multiply warped product space with nonpositive scalar curvature, International Journal of Geometric Methods in Modern

Physics (SCI-Exp, Q2, Imp. Factor-1.874), 16(10) (2019), 1950162 (14 pages)

https://doi.org/10.1142/S0219887819501627

• Buddhadev Pal and Pankaj Kumar, A family of multiply warped product semi-Riemannian Einstein metrics, International Journal of Geometric mechanics (SCI-Exp, Q3, Imp. Factor-0.857), 2020, 12(4), 553-562. http://dx.doi.org/10.3934/jgm.2020017

• Buddhadev Pal and Pankaj Kumar, Einstein, Poisson warped product space, Classical and

Quantum Gravity (SCI, Q1, Imp. Factor-3.528), 38(2021), 065004 (29pp).

http://dx.doi.org/10.1088/1361-6382/abd7c0

• Buddhadev Pal and Pankaj Kumar, On Einstein warped product space with respect to

 semi symmetric metric connection, Hacettepe Journal of Mathematics and Statistics

(SCI-Exp, Q3, Imp. Factor-0.929), 50(5) (2021), 1477-1490. http://dx.doi.org/10.15672/hujms.755030

• Buddhadev Pal and Pankaj Kumar, Characterization of Einstein Poisson warped product space, Afrika Matematika (Scopus, Q3, Imp. Factor-0.929), 33(4) (2022), (16pp).

https://doi.org/10.1007/s13370-022-01029-1

• Buddhadev Pal and Pankaj Kumar, Einstein warped product spaces on

Lie groups, CUBO, A Mathematical Journal (ESCI, Q4, Imp. Factor-0.988), 3(24) (2022),

485-500.

https://doi.org/10.56754/0719-0646.2403.0485

• Buddhadev Pal and Pankaj Kumar, On Einstein Riemannian Poisson warped product space, Filomat, (SCI, Q2, Imp. Factor-0.988), 36(17) (2022), 5957-5972.

https://doi.org/10.2298/FIL2217957P

• Buddhadev Pal and Pankaj Kumar, Ricci-Bourguignon solitons on

warped product space, Reports on Mathematical Physics, (SCI-Exp, Q3, Imp. Factor-0.8),

92(1) (2023)

Conferences/Webinars

• Presented a paper entitled Compact Einstein multiply warped product space with nonpositive scalar curvature, in the National Conference on Recent Trends in Geometry and their Applications organized by Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi during February 08 -09, 2020.

• Presented a paper entitled A family of multiply warped product semi-Riemannian Einstein metrics, in the 36th Annual National Conference of the Mathematical Society – Banaras Hindu University organized by Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi during February 06 - 07, 2021.

• Presented a paper entitled Einstein Poisson warped product space, in the International Hazar Scientific Researches Conference - II organized by Khazar University, Baku, Azerbaijan during April 10 - 12, 2021.

• Presented a paper entitled On Einstein warped product space with respect to semi symmetric metric connection, in the 27th International Conference of International Academy of Physical Sciences organized by Department of Mathematics and Statistics Central University of Punjab, Bathinda - India during October 26 -28, 2021.

• Presented a paper entitled On Riemannian Poisson warped product space, in International Conference of Differential Geometry and Dynamical Systems (DGDS 2022) organized by University Geometry and Dynamical Systems (DGDS 2022) organized by University Polithehnica of Bucharest and the Balkan Society of Geometers (Romania) during September 01-04, 2022.

Certifications

• Annual Foundation School - I organized by Bhaskaracharya Pratishthana, Pune, with National center for Mathematics, during December 04 - 30, 2017.

• Annual Foundation School - II organized by Central University of Rajasthan, Ajmer with National center for Mathematics, during December 03 - 29, 2018.

• Exploring some Applications of Mathematical Sciences, organized by Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi during January 19 -20, 2019.

• CIMPA School on Finsler Geometry and Applications, organized by DCT - CIMS, Institute of Science, Banaras Hindu University, Varanasi during December 05 -15, 2019.

• NACI - TMC Summer School on Differential Geometry, organized by Central University of Punjab, Bathinda during July 05 -24, 2021.

Area of Interest

• Differential geometry
• Poisson geometry
• Finsler geometry

Operating Systems and Tools

• LaTex
• Sci Lab
• Microsoft Windows