shanmukha

@gmit.ac.in

Assistant Professor, Department of Mathematics, GMIT Davangere
GM Institute of Technology

shanmukha


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https://researchid.co/meshanmukha

RESEARCH INTERESTS

Differential Geometry
8

Scopus Publications

54

Scholar Citations

5

Scholar h-index

1

Scholar i10-index

Scopus Publications

  • Some results on Kenmotsu space forms
    Shanmukha B, Suhad Ali Osman Abdallah, N. S. Abd El-Gawaad
    Journal of Applied Analysis, 2026
    The object of the present paper is to study Kenmotsu space forms satisfying pseudosymmetric, Ricci-pseudosymmetric and locally-ϕ-symmetric. Further we study the quasi-conformal flat and quasi-conformal semisymmetric Kenmotsu space forms.
  • Dynamical analysis of hearing loss due to mumps virus with Caputo fractional derivative
    B. Shanmukha
    International Journal of Modeling Simulation and Scientific Computing, 2024
    Mumps is the most common disease for children, which causes hearing loss in all auditory systems. WHO initiated compulsory vaccination for children who are at age of 12 months to 12 years, since 1967. Children must take two doses of vaccination for mumps. The dynamics of the system describing the mumps transmission is studied in this work. The main aim is to elucidate the nonlinear behavior of the system which can provide insights into the long-term effects of Mumps infection on auditory function. As the fractional-order derivative preserves the impact of system memory, we employ the Caputo fractional derivative as the dynamical system describing modeling to simulate hearing loss in children brought on by the mumps virus. The boundedness existence of the solution and stability analysis of the dynamical system are derived in the framework. The result is derived using a well-known numerical method to capture the corresponding consequences and predict the future consequence of the dynamical system associated with parameters. To testify to the importance of the generalizing classical model with a fractional operator, we plot 2D graphs. This study helps to researcher beginners to understand the essential and fundamental tools while investigating real-world problems.
  • Bochner formula in generalized (k,μ)-space forms
    Shanmukha B
    Journal of Applied Analysis, 2023
    In this article, we studied Green’s theorem and the Bochner formula. Further, we apply the Bochner formula to generalized ( k , μ ) {(k,\mu)} -space forms and show that the generalized ( k , μ ) {(k,\mu)} space form is either isometric to a sphere or a certain warped product under some geometric conditions.
  • M-projective curvature tensor on an (LCS)2n+1-manifold
    B. Shanmukha, V. Venkatesha
    Journal of Applied Analysis, 2021
    In this paper, we study M-projective curvature tensors on an ( LCS ) 2 ⁢ n + 1 {(\\mathrm{LCS})_{2n+1}} -manifold. Here we study M-projectively Ricci symmetric and M-projectively flat admitting spacetime.
  • Some Ricci solitons on Kenmotsu manifold
    B. Shanmukha, V. Venkatesha
    Journal of Analysis, 2020
    In the present frame work, we study the properties of $$\\eta$$ η -Ricci soliton on Kenmotsu manifold and also analysed the generalized gradient Ricci soliton equation satisfying some conditions.
  • Invariant submanifolds of LP-Sasakian manifolds
    V. Venkatesha, Shanmukha Basavarajappa
    Khayyam Journal of Mathematics, 2020
    The object of the present paper is to study some geometric conditions for an invariant submanifold of an LP-Sasakian manifold to be totally geodesic. Further we consider concircular curvature tensor satisfying some geometric conditions of an invariant submanifold of an LP-Sasakian manifold to be totally geodesic. In extension, we build an example of LP-Sasakian manifold to verify our main result totally geodesic.
  • LP-sasakian manifold admitting C-bochner curvature tensor
    Palestine Journal of Mathematics, 2020
  • Projective curvature tensor on generalized (k, µ)-space forms
    Italian Journal of Pure and Applied Mathematics, 2019

RECENT SCHOLAR PUBLICATIONS

  • Dynamical analysis of hearing loss due to mumps virus with Caputo fractional derivative
    B Shanmukha
    International Journal of Modeling, Simulation, and Scientific Computing 15 … , 2024
    2024.0
    Citations: 1
  • Bochner formula in generalized (k, μ)-space forms
    B Shanmukha
    Journal of Applied Analysis 29 (2), 323-328 , 2023
    2023.0
  • M-projective curvature tensor on an (LCS) 2n+1 -manifold.
    B Shanmukha, V Venkatesha
    Journal of Applied Analysis 27 (2) , 2021
    2021.0
    Citations: 2
  • Some Ricci solitons on Kenmotsu manifold
    B Shanmukha, V Venkatesha
    The Journal of Analysis 28 (4), 1155-1164 , 2020
    2020.0
    Citations: 9
  • Some results on generalized Sasakian space forms
    SB Venkatesha
    Applied Mathematics and Nonlinear Sciences 5 (1), 85-92 , 2020
    2020.0
    Citations: 9
  • Invariant submanifolds of LP-Sasakian manifolds
    V Venkatesha, S Basavarajappa
    Khayyam Journal of Mathematics 6 (1), 16-26 , 2020
    2020.0
    Citations: 16
  • LP-Sasakian Manifold Admitting C-Bochner Curvature Tensor
    SB Venkatesha
    Palestine Journal of Mathematics 9 (1), 396–401 , 2020
    2020.0
  • Certain Curvature Conditions on N (k)-Paracontact Metric Manifolds
    BP Murthy, B Shanmukha
    arXiv preprint arXiv:1901.07895 , 2019
    2019.0
  • Projective curvature tensor on generalized (k, µ)-space forms
    B Shammukha, V Venkatesha
    Italian J. Pure Appl. Math 12, 810-850 , 2019
    2019.0
    Citations: 3
  • W2-Curvature Tensor on Generalized Sasakian Space Forms
    S B, Venkatesha
    CUBO, A Mathematical Journal 20 (1), 17–29-17–29 , 2018
    2018.0
  • Some results on generalized (k, μ)-space forms
    B Shanmukha, Venkatesha and SV Vishunuvardhana
    New Trends in Mathematical Sciences 6 (3), 48-56 , 2018
    2018.0
    Citations: 2
  • SOME RESULTS ON GENERALIZED SASAKIAN SPACE FORMS WITH QUARTER SYMMETRIC METRIC CONNECTION
    BSAND VENKATESHA
    Asian Journal of Mathematics and Computer Research 25 (3), 183-191 , 2018
    2018.0
    Citations: 5
  • Venkatesha and SV Vishunuvardhana
    B Shanmukha
    Some results on generalized (k, µ)-space forms, 48-56 , 2018
    2018.0
    Citations: 7
  • 𝑴-Projective Curvature Tensor on Lorentzian 𝜶-Sasakian Manifolds
    venkatesha and shanmukha B.
    global journal of pure and applied mathematics 13 (7), 2849-2858 , 2017
    2017.0
  • Certain Curvature Tensor On Lorentzian α-Sasakian Manifolds
    venkatesha and shanmukha B
    Procedings of International Conference On ICDGAFM, 226-232 , 2016
    2016.0
  • Certain results on Para-Sasakian manifold admitting a quarter-symmetric metric connection
    VSVSB Venkatesha
    Proceedings of NCPAM, 82-89 , 2015
    2015.0
  • Some results on Kenmotsu space forms
    B Shanmukha, SAO Abdallah, NS Abd El-Gawaad
    Journal of Applied Analysis , 0

MOST CITED SCHOLAR PUBLICATIONS

  • Invariant submanifolds of LP-Sasakian manifolds
    V Venkatesha, S Basavarajappa
    Khayyam Journal of Mathematics 6 (1), 16-26 , 2020
    2020.0
    Citations: 16
  • Some Ricci solitons on Kenmotsu manifold
    B Shanmukha, V Venkatesha
    The Journal of Analysis 28 (4), 1155-1164 , 2020
    2020.0
    Citations: 9
  • Some results on generalized Sasakian space forms
    SB Venkatesha
    Applied Mathematics and Nonlinear Sciences 5 (1), 85-92 , 2020
    2020.0
    Citations: 9
  • Venkatesha and SV Vishunuvardhana
    B Shanmukha
    Some results on generalized (k, µ)-space forms, 48-56 , 2018
    2018.0
    Citations: 7
  • SOME RESULTS ON GENERALIZED SASAKIAN SPACE FORMS WITH QUARTER SYMMETRIC METRIC CONNECTION
    BSAND VENKATESHA
    Asian Journal of Mathematics and Computer Research 25 (3), 183-191 , 2018
    2018.0
    Citations: 5
  • Projective curvature tensor on generalized (k, µ)-space forms
    B Shammukha, V Venkatesha
    Italian J. Pure Appl. Math 12, 810-850 , 2019
    2019.0
    Citations: 3
  • M-projective curvature tensor on an (LCS) 2n+1 -manifold.
    B Shanmukha, V Venkatesha
    Journal of Applied Analysis 27 (2) , 2021
    2021.0
    Citations: 2
  • Some results on generalized (k, μ)-space forms
    B Shanmukha, Venkatesha and SV Vishunuvardhana
    New Trends in Mathematical Sciences 6 (3), 48-56 , 2018
    2018.0
    Citations: 2
  • Dynamical analysis of hearing loss due to mumps virus with Caputo fractional derivative
    B Shanmukha
    International Journal of Modeling, Simulation, and Scientific Computing 15 … , 2024
    2024.0
    Citations: 1
  • Bochner formula in generalized (k, μ)-space forms
    B Shanmukha
    Journal of Applied Analysis 29 (2), 323-328 , 2023
    2023.0
  • LP-Sasakian Manifold Admitting C-Bochner Curvature Tensor
    SB Venkatesha
    Palestine Journal of Mathematics 9 (1), 396–401 , 2020
    2020.0
  • Certain Curvature Conditions on N (k)-Paracontact Metric Manifolds
    BP Murthy, B Shanmukha
    arXiv preprint arXiv:1901.07895 , 2019
    2019.0
  • W2-Curvature Tensor on Generalized Sasakian Space Forms
    S B, Venkatesha
    CUBO, A Mathematical Journal 20 (1), 17–29-17–29 , 2018
    2018.0
  • 𝑴-Projective Curvature Tensor on Lorentzian 𝜶-Sasakian Manifolds
    venkatesha and shanmukha B.
    global journal of pure and applied mathematics 13 (7), 2849-2858 , 2017
    2017.0
  • Certain Curvature Tensor On Lorentzian α-Sasakian Manifolds
    venkatesha and shanmukha B
    Procedings of International Conference On ICDGAFM, 226-232 , 2016
    2016.0
  • Certain results on Para-Sasakian manifold admitting a quarter-symmetric metric connection
    VSVSB Venkatesha
    Proceedings of NCPAM, 82-89 , 2015
    2015.0
  • Some results on Kenmotsu space forms
    B Shanmukha, SAO Abdallah, NS Abd El-Gawaad
    Journal of Applied Analysis , 0