Professor Krishan L. Duggal: A Biographical Note

Year 2023, Volume: 16 Issue: 1, 1 - 3, 30.04.2023

R. Sharma , Bayram Şahin

https://doi.org/10.36890/iejg.1253398

Abstract

In this note, we present a biographical sketch of the life and academic contributions of late Professor Krishan L. Duggal. His contributions span from Riemannian and Lorentzian geometries of manifolds with various structural groups of the tangent bundle, Lightlike curves and submanifolds, Cauchy-Riemann geometry, Symmetries of semi-Riemannian manifolds, to Killing horizons. In particular, his approach to the study of lightlike submanifolds is remarkable and drawn considerable interest of many geometers.

Keywords

CR-structure, lightlike submanifolds, conformal geometry, Lorentzian geometry, general relativity

Supporting Institution

University Of New Haven

References

• [1] Barletta, E., Dragomir, S. and Duggal, K.L.: Foliations in Cauchy-Riemann Geometry, Mathematical Surveys and Monographs, American Mathematical Society, 2007.
• [2] Beem, J.K. and Duggal, K.L.: Differential geometry and Mathematical Physics, Contemporary Mathematics, Volume 170, American Mathematical Society, 1994.
• [3] Bejancu, A.: Lightlike curves in Lorentzian manifolds, Publicationes Math. Debrecen 44 (1994), 145-155.
• [4] Bejancu, A. and Duggal, K.L.: Degenerate hypersurfaces of semi-Riemannian manifolds, Buletinul Institului Politehnic, Iasi 37 (1991),3-22.
• [5] Duggal, K.L.: Almost Ricci solitons and physical applications, Internat. Electron. J. Geom. 10 (2017), 1-10.
• [6] Duggal, K.L.: A new class of contact pseudo Framed manifolds with applications, Internat. J. Math. Math. Sci. (2021), 1-9, doi:10.1155/2021/6141587.
• [7] Duggal, K.L. and Bejancu, A.: Lightlike submanifolds of Semi-Riemannian Manifolds and Applications, Mathematics and Its Applications, Volume 364, Springer, 2010.
• [8] Duggal, K.L. and Jin, D.H.: Null curves and hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007.
• [9] Duggal, K. L. and Şahin, B. Screen conformal half-lightlike submanifolds. Int. J. Math. Math. Sci. 65-68, (2004), 3737–3753.
• [10] Duggal, K. L. and Şahin, B. Screen Cauchy Riemann lightlike submanifolds. Acta Math. Hungar. 106 (1-2), (2005), 137–165.
• [11] Duggal, K. L. and Şahin, B. Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. Acta Math. Hungar. 112(1-2),(2006), 107–130.
• [12] Duggal, K. L. and Şahin, B. Lightlike submanifolds of indefinite Sasakian manifolds. Int. J. Math. Math. Sci. 2007, Art. ID 57585, 21 pp.
• [13] Duggal, K. L. and Şahin, B. Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds. Acta Math. Hungar. 122(1-2), (2009), 45–58.
• [14] Duggal, K.L. and Şahin, B.: Differential geometry of Lightlike Submanifolds, Frontiers in Mathematics, Springer, 2010.
• [15] Duggal, K.L. and Sharma, R.: Lorentzian framed structures in general relativity, General Relativity and Gravitation 19 (1986), 71-77.
• [16] Duggal, K.L. and Sharma, R.: Conformal collineations and anisotropic fluids in general relativity, Journal of Mathematical Physics 27(1986), 2511-2513.
• [17] Duggal, K.L. and Sharma, R.: Mixed foliate CR-submanifolds of indefinite complex space-forms, Annali di Matematica Pura ed Applicata 149 (1987), 103-111.
• [18] Duggal, K.L. and Sharma, R.: Ricci curvature inheriting symmetries of semi-Riemannian manifolds, Contemporary Mathematics (American Mathematical Society) 170 (1994), 215-224.
• [19] Duggal, K.L. and Sharma, R. : Symmetries of Spacetimes and Riemannian Manifolds, Mathematics and its Applications, Vol. 487, Kluwer Academic Press,1999 (Taken over by Springer-Science).
• [20] Duggal, K.L. and Sharma, R. : Recent Advances in Riemannian and Lorentzian Geometries, Contemporary Mathematics, Volume 337, American Mathematical Society.
• [21] Kupeli, D.N.: Singular Semi-Riemannian Geometry, Vol. 366, Kluwer Academic Press, 1996.
• [22] Sharma, R.: Cauchy-Riemann Submanifolds of Semi-Riemannian Manifolds with Application to Relativity and Hydrodynamics, Ph.D. dissertation, University of Windsor, Ontario, Canada, 1986.
• [23] Sharma, R. and Duggal, K.L.: Solutions of Einstein’s equations with conformal symmetries and a contact slice, Nonlinear Analysis, Theory, Methods and Applns. 71 (2009), e701-705.