Tohoku Mathematical Journal
2024
June
SECOND SERIES VOL. 76, NO. 2

Tohoku Math. J.
76 (2024), 199-215

Title ON GEODESICS OF FRAMED SURFACES IN THE EUCLIDEAN 3-SPACE

Dedicated to Professor Osamu Saeki on his sixtieth birthday
Author Masatomo Takahashi

(Received August 22, 2022, revised October 17, 2022)
Abstract. We would like to define the notion of geodesics for surfaces with singular points. As surfaces with singular points, we consider framed surfaces. Moreover, as curves with singular points, we consider framed curves. Then we give a definition of geodesic as a framed curve of a framed surface. We investigate properties of the geodesic and give examples.

Mathematics Subject Classification. Primary 57R45; Secondary 53A05, 58K05.
Key words and phrases. Geodesics, framed surfaces, framed curves, singular points.

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