Conformally flat immersions in codimension two

✍ Scribed by Maria Helena Noronha

• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 558 KB
• Volume: 23
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147397

✦ Synopsis

The aim of this paper is to study the local geometry of a conformally fiat manifold which admits local isometric immersions in some Euclidean space with low codimension.

Moreover, if n >~ 4, (ii) is consequence of (i).

A nice characterization in terms of sectional curvature is given by Kulkarni in [6]:

1.3. THEOREM. If n >~ 4, M n is conformally flat if and only if for any orthogonal vectors X1, X2, X3, X46 TxM we have K(X 1 , X 2) q-K(X3, X4) = K(Xx, X3) + K(X 2, X4),