The curvature Veronese of a 3-manifold immersed in Euclidean space
Rosane Binotto, Sueli I. R. Costa, M. C. Romero Fuster · Contemporary mathematics - American Mathematical Society · 2016
We study the behaviour of the curvature locus of a 3 3 -manifold immersed in R n , n ≥ 5 \mathbb {R}^n, n \geq 5 , describing their possible topological types at the different points of a 3 3 -manifold immersed in R 6 \mathbb {R}^6 . We analyze the connections between the structure of the curvature locus with the behaviour of the principal configurations associated to normal fields on the 3 3 -manifold, as well as with the local convexity of the 3 3 -manifold.