Dorin Andrica, Dana Mangra and Cornel Pintea: The circular Morse-Smale characteristic of closed surfaces, p.235-242

Abstract:

In this paper we first compute the circular version of the Morse-Smale characteristic of all closed surfaces. We also observe that the critical points of the real valued height functions alongside those of some $S^1$ valued functions on a surface $\Sigma\subset\mathbb{R}^3$, are the characteristic points with respect to some involutive distributions. We finally study the size of the characteristic set of the compact orientable surface of genus $g$, embedded in a certain way in the first Heisenberg group, with respect to the horizontal distribution of the Heisenberg group.

Key Words: Morse functions, circular Morse-Smale characteristic, characteristic points.

2000 Mathematics Subject Classification: Primary: 58E05;
Secondary: 658K45, 58K05.

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