Immersions preserved under rotations with totally reducible focal set

Abstract

In [1] Carter and the author introduced the idea of an immersion f : M ^m → Rⁿ with totally reducible focal set (TRFS). Such an immersion has the property that, for all p ∈ M, the focal set with base p is a union of hyperplanes in the normal plane to f(M) at f(p). Here we show that if we take two immersions with TRFS then we can construct new immersions with TRFS. In particular, rotating an immersion with TRFS about an axis gives a new immersion with TRFS. © TÜBİTAK.