S.M. Bhati This email address is being protected from spambots. You need JavaScript enabled to view it.1, G. Murali2, and Ch. Sanjay3

1Maratha Vidya Prasarak Samaj’s KBT College of Engineering, Nashik - 422013, India.
2Department of Mathematics, Malla Reddy University, Hyderabad-500100, India.
3Department of Industrial Engineering, King Saud University, Saudi Arabia.


 

Received: June 8, 2021
Accepted: August 13, 2021
Publication Date: November 10, 2021

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.


Download Citation: ||https://doi.org/10.6180/jase.202208_25(4).0011  


ABSTRACT


we define a second order tensor E of rank 2 for the electric flux called the electric flux tensor and obtain the law of electric fields in the space time system with respect to any frame of reference, using Bianchi identities of Riemannian Geometry similar to that of time variant Maxwell’s law of electric fields. Finally, it may be seen that the time variant Maxwell’s law of electric fields will include as a special case of our results.


Keywords: Bianchi Identities, electric flux, Maxwell’s equations for electric fields, Riemannian geometry


REFERENCES


  1. [1] Z. Ahsan, (2017) “Tensors: Mathematics of Differential Geometry and Relativity, PHI Learning Pvt" Ltd., Delhi (December 2017, Second Printing):
  2. [2] L. Bianchi, (1902) “Sui simboli a quattro indici e sulla curvatura di Riemann" Rend. Acc. Naz. Lincei 11(5):3–7.
  3. [3] J. B. Davies, (1988) “New curvature-torsion relations through decomposition of the Bianchi Identities" Foundations of physics 18(5): 563–569. DOI: 10 . 1007 /BF00732746.
  4. [4] S. K. Stein. Calculus and analytic geometry. McGraw-Hill Companies, 1987.
  5. [5] K. Yano. Integral formulas in Riemannian geometry. 1. Marcel Dekker, 1970.
  6. [6] S. BHATI, G. MURALI, G. DEEPA, and C. SANJAY, “Continuity Equations in Fluid Dynamics and Bianchi Identities":


    
 

0.7
2020CiteScore
 
 
33rd percentile
Powered by  Scopus

SCImago Journal & Country Rank

Enter your name and email below to receive latest published articles in Journal of Applied Science and Engineering.