| Abstract: | Circularm-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct
an example of a four-dimensional manifoldM
4 with boundary ∂M
4 that satisfies the condition ξ(∂M
4)=ξ(M
4,∂M
4)=0 but does not contain any circularm-function. We prove that a manifold with boundaryM
n
(n≥5) such that ξ(∂M
n
, ∂M
n
)=0 always contains a circularm-function without critical points in the interior manifold.
Sukhumi Branch of the Tbilisi University, Sukhumi. Translated from Ukrainskii Matermaticheskii Zhurnal, Vol. 46, No. 6, pp.
776–781, June, 1994. |
