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SEMI-INVARIANT SUBMANIFOLDS OF (LCS)<sub>n</sub>-MANIFOLD
Bagewadi, Channabasappa Shanthappa,Nirmala, Dharmanaik,Siddesha, Mallannara Siddalingappa Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.4
In this paper the decomposition of basic equations of $(LCS)_n$-manifolds is carried out into horizontal and vertical projections. Further, we study the integrability of the distributions $D,D{\oplus}[{\xi}]$ and $D^{\perp}$ totally geodesic of semi-invariant submanifolds of $(LCS)_n$-manifold.
Solitons of K\"{A}hlerian Norden space-time manifolds
Praveena Manjappa Mundalamane,Bagewadi Channabasappa Shanthappa,Mallannara Siddalingappa Siddesha 대한수학회 2022 대한수학회논문집 Vol.37 No.3
We study solitons of K\"{a}hlerian Norden space-time manifolds and Bochner curvature tensor in almost pseudo symmetric K\"{a}hlerian space-time manifolds. It is shown that the steady, expanding or shrinking solitons depend on different relations of energy density/isotropic pressure, the cosmological constant, and gravitational constant.
From the Eisenhart Problem to Ricci Solitons in Quaternion Space Forms
Praveena, Mundalamane Manjappa,Bagewadi, Channabasappa Shanthappa Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.2
In this paper we obtain the condition for the existence of Ricci solitons in nonflat quaternion space form by using Eisenhart problem. Also it is proved that if (g, V, ${\lambda}$) is Ricci soliton then V is solenoidal if and only if it is shrinking, steady and expanding depending upon the sign of scalar curvature. Further it is shown that Ricci soliton in semi-symmetric quaternion space form depends on quaternion sectional curvature c if V is solenoidal.