shanmukha
Verified @gmail.com
Assistant Professor, Department of Mathematics, GMIT Davangere
GMIT, Davangere
RESEARCH INTERESTS
Differential Geometry
10
Scopus Publications
47
Scholar Citations
4
Scholar h-index
1
Scholar i10-index
Scopus Publications
- M-projective curvature tensor on an (LCS)<inf>2n+1</inf>-manifold
B. Shanmukha and V. Venkatesha
Walter de Gruyter GmbH
Abstract 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 and V. Venkatesha
Springer Science and Business Media LLC
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 and Shanmukha Basavarajappa
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
- Hybrid cross layer fault resilient energy efficient data transmission for underwater acoustic sensor networks
K. Vidyalakshmi, M.Siddappa and B.Shanmukha
Blue Eyes Intelligence Engineering and Sciences Engineering and Sciences Publication - BEIESP
Under water acoustic sensor network is the unique case of wireless sensor network in which the physical characteristics limits the capability of sensor network due to various problems like Doppler-spreads, medium significnt delay, Double-side spreading, limited bandwidth and frequencyselective fading. Ensuring QOS is very challenging problem in acoustic sensor networks. In this work, a QOS centric hybrid routing protocol with consideration of fault resilience is proposed. The solution use the parameters of the network at all Application Layer, Network Layer, MAC Layer, and PHY Layer, which are the different layers of IEEE 802.15.4 protocol stack, thus calculating Node selection score which helps in identifying the best forwarding node for a constrained reliable data transmission. The solution involves dynamic link quality estimation, congestion awareness, packet injection ratio estimation and physical switching that cumulatively ensures fault-resilient and QoS delivery over acoustic sensor network. - Hybrid cross layer mechanism for high reliability in under water wireless sensor network
Vidyalakshmi. K, M. Siddappa, and B. Shanmukha
IEEE
Under water sensor network finds lot of applications in sea environment monitoring. Tsunami like conditions can be monitored and reported earlier so that people on shores can be safe. Due to nature of medium, the data delivery ratio in under water sensor networks is very low. The various problems in the underwater sensor networks are medium significant delay, Double-side-spreading, Doppler- spreads, frequency-selective fading and limited bandwidth. These problems reduce the data delivery ratio. In this work hybrid cross layer method with mechanisms in physical, data link and routing layer are proposed to increase the reliability of underwater wireless sensor networks. - Projective curvature tensor on generalized (k, µ)-space forms
- Mathematical modeling of zika virus disease with nonlinear incidence and optimal control
Naba Kumar Goswami, Akhil Kumar Srivastav, Mini Ghosh, and B Shanmukha
IOP Publishing
The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. However, there is documented evidence of sexual transmission of this disease too. In this paper, a nonlinear mathematical model for Zika virus by considering nonlinear incidence is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The stability of the different equilibria of the model is discussed in detail. When the basic reproduction number R0 1, we have endemic equilibrium which is locally stable under some restriction on parameters. Further this model is extended to optimal control model and is analyzed by using Pontryagin's Maximum Principle. It has been observed that optimal control plays a significant role in reducing the number of zika infectives. Finally, numerical simulation is performed to illustrate the analytical findings.
RECENT SCHOLAR PUBLICATIONS
- Some results on Kenmotsu space forms
SAO Abdallah, NSA El-Gawaad
Journal of Applied Analysis 2025 - 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 - Bochner formula in generalized (k, μ)-space forms
B Shanmukha
Journal of Applied Analysis 29 (2), 323-328 2023 - M-projective curvature tensor on an (LCS)2n+1-manifold
B Shanmukha, V Venkatesha
Journal of Applied Analysis 27 (2), 283-288 2021 - Some Ricci solitons on Kenmotsu manifold
B Shanmukha, V Venkatesha
The Journal of Analysis 28 (4), 1155-1164 2020 - Some results on generalized Sasakian space forms
SB Venkatesha
Appl. Math. Nonlinear Sci 5 (1), 85-92 2020 - Invariant submanifolds of LP-Sasakian manifolds
V Venkatesha, S Basavarajappa
Khayyam Journal of Mathematics 6 (1), 16-26 2020 - LP-Sasakian Manifold Admitting C-Bochner Curvature Tensor
SB Venkatesha
Palestine Journal of Mathematics 9 (1), 396–401 2020 - Certain Curvature Conditions on N (k)-Paracontact Metric Manifolds
BP Murthy, B Shanmukha
arXiv preprint arXiv:1901.07895 2019 - Projective curvature tensor on generalized (k, )-space forms
B Shammukha, V Venkatesha
Italian J. Pure Appl. Math 12, 810-850 2019 - W2-Curvature Tensor on Generalized Sasakian Space Forms
S B, Venkatesha
CUBO, A Mathematical Journal 20 (1), 17–29-17–29 2018 - Some results on generalized (k, μ)-space forms
B Shanmukha, Venkatesha and SV Vishunuvardhana
New Trends in Mathematical Sciences 6 (3), 48-56 2018 - 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 - Venkatesha and SV Vishunuvardhana
B Shanmukha
Some results on generalized (k, )-space forms, 48-56 2018 - 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 - Certain Curvature Tensor On Lorentzian α-Sasakian Manifolds
venkatesha and shanmukha B
Procedings of International Conference On ICDGAFM, 226-232 2016 - Certain results on Para-Sasakian manifold admitting a quarter-symmetric metric connection
VSVSB Venkatesha
Proceedings of NCPAM, 82-89 2015
MOST CITED SCHOLAR PUBLICATIONS
- Invariant submanifolds of LP-Sasakian manifolds
V Venkatesha, S Basavarajappa
Khayyam Journal of Mathematics 6 (1), 16-26 2020
Citations: 14 - Some results on generalized Sasakian space forms
SB Venkatesha
Appl. Math. Nonlinear Sci 5 (1), 85-92 2020
Citations: 9 - Venkatesha and SV Vishunuvardhana
B Shanmukha
Some results on generalized (k, )-space forms, 48-56 2018
Citations: 7 - Some Ricci solitons on Kenmotsu manifold
B Shanmukha, V Venkatesha
The Journal of Analysis 28 (4), 1155-1164 2020
Citations: 5 - 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
Citations: 4 - Projective curvature tensor on generalized (k, )-space forms
B Shammukha, V Venkatesha
Italian J. Pure Appl. Math 12, 810-850 2019
Citations: 3 - M-projective curvature tensor on an (LCS)2n+1-manifold
B Shanmukha, V Venkatesha
Journal of Applied Analysis 27 (2), 283-288 2021
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
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
Citations: 1