Journal of the Ramanujan Mathematical Society

M. Nagaraj ¹, R. Srinivasa Murthy ²

Affiliations
1 Department of Mathematics, Bangalore University, Bangalore-560 001, IN
2 S.Nijalingappa College, Bangalore-56O 001, IN

Abstract

We associate characteristic equations with a Farey fraction and define fundamental solutions for them. The concept of a tribe is defined for the fraction with the help of these solutions, and some interesting results about these tribes are obtained. We also study the nature of symmetrical elements about a fraction.

Keywords

Farey Fractions, Tribe of Farey Fractions, Properties of Tribes.

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K. E. Bakkesa Swamy ¹, M. Nagaraj ¹

Affiliations
1 Department of Mathematics, Bangalore University, Bangalore-560 001, IN

Abstract

Hamiltonian metrics are introduced on an almost quaternion real manifold. It is proved that every almost quaternion para-compact real manifold admits a Hamiltonian metric. It is established that there is a bijective correspondence between the set of all Hamiltonj.an metrics on an almost quaternion real manifold of dimension 4m with respect to the -canonical almost quaternion structure and the homogeneous space Θ{GL(m,H)}/Θ{Sp(m)}.

Keywords

Almost Quaternion Structure, Homogeneous Manifolds.

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