In this paper, we investigate the curvature properties of a family of four-dimensional Walker manifolds. We establish the existence of non-trivial Ricci solitons on this family of manifolds and provide explicit examples to illustrate the results.
The object of the present article is to characterize Yamabe solitons admitting torse-forming vector fields with supporting non-trivial examples. Quotient Yamabe almost solitons with potential vector fields as infinitesimal harmonic transformations are studied. In addition, a triviality result of quotient almost Yamabe soliton is established using an integral inequality.
The set CS(L) of all convex sublattices of a lattice L, excluding & empty;, was studied by S. Lavanya and S. P. Bhatta using the partial order <=, defined as follows: for A, B is an element of CS(L), A <= B if and only if 'for each a is an element of A, there is b is an element of B such that a <= b' and 'for each b is an element of B, there is a is an element of A such that a <= b'. They showed that (CS(L), <=) is a lattice such that both L and CS(L) lie in the same equational class. Also, they obtained many significant results concerning CS(L). The present paper generalizes many of these results along with some related results of others, from lattices to trellises, by introducing the notion of 'strongly-convex subtrellises' in trellises in place of 'convex sublattices' in lattices.
In this paper, we show that if (A, ||.||(p)), 0 < p <= 1, is a unital semi-simple p-Banach algebra such that, for every non-zero idempotent element u of A, Sp(Au) (x) is finite for each x is an element of partial derivative(G(A(u)), where A(u) = uAu, then A is finite-dimensional. As a consequence, we obtain that a spectrally finite p-Banach algebra is finite-dimensional modulo its Jacobson radical. Similar results are also obtained with the spectrally convex property.
In this paper, we investigate the geometric aspects of the action of SL(3, R) subgroups in the real projective plane from an Erlangen perspective. Specifically, the study investigates the projective action of the subgroups of SL(3, R) on the non-degenerate conics in RP2, which is obtained as the two-dimensional homogeneous space of SL(3, R). By investigating the subgroup of SL(3, R) that preserves the projective unit circle, a connection is established between this subgroup and the Lie group SL(2, R). Expanding upon V. Kisil's research on the EPH classification of geometries related to the Mobius action of SL(2, R), this paper extends the analysis to the projective action of SL(3, R), with the adjoint representation of SL(2, R) playing a significant role. Mappings from the elliptic, parabolic, and hyperbolic (abbreviated as EPH) upper half plane to the interior, boundary, and exterior of the projective unit circle are investigated. A unified expression for isomorphisms facilitates a cohesive framework for analyzing these mappings. Furthermore, the study investigates Mobius -invariant cycle images, demonstrating that elliptic and hyperbolic cycles correspond to ellipses and hyperbolas, respectively, while parabolic cycles map to the projective unit circle.
