SCALAR CURVATURES ON SU(3)/T(k, l)

Abstract

Abstract. In this paper, we estimated the Ricci curvature and the scalar curvature on SU (3)/T (k, l) under the condition (k, l) ∈ R 2 (|k| + |l| = 0), where the four isotropy irreducible representations in SU (3)/T (k, l) are, not necessarily, mutually equivalent or inequivalent.

Variations of the Length Integral

“…The second variation is expressed in terms of the sectional curvature ( [1,2,3,4]) and the variation vector field along the curve τ = x t (0 ≤ t ≤ 1). And then, we get a necessary and sufficient condition for the second variation (d 2 L(s)/ds 2 ) s=0 to be 0.…”