The Journal of the Indian Mathematical Society

R. S. Mishra ¹

Affiliations
1 Lucknow University, IN

Abstract

Five families of ruled surfaces through a line of a rectilinear congruence obtained by the repeated application of the operation of forming the Jacobian from Sannia's quadratic forms f ≡ G_aβ du^a du^β and φ ≡ε _aβ du^a du^β were studied in detail by Ogura [7, 8], Hayashi [2], Ram Behari [9] and Mishra [4]; and those from Kummer's quadratic forms f ≡ G_aβ du^a du^β and θ ≡ μ_aβ du^a du^β by Mishra [5]. It is the purpose of the present paper to study the ruled surfaces obtained by the repeated application of the# operation of forming the Jacobian from the quadratic forms θ and φ.

Full Text

     

R. S. Mishra ¹

Affiliations
1 Banaras Hindu University, Varanasi, IN

Abstract

An even-dimensional differentiable manifold V_2m on which there are defined a tensor field F of the type (1,1) and a metric-tensor field g, satisfying for arbitrary vector fields λ, μ, v, . . . ∈ V_2m,
F²=-I_2m, (1.1a)
'F(λ,μ)=g(Fλ,μ)=-'F(μ,μ), (1.1b)
is called an almost Hermite manifold with the almost Hermite structure {F,g} (Helgason, 1960; Yano, 1965; Mishra, 1984, p. 67).

Full Text