An elementary proof of the classification of surfaces in the projective 3-space

Creighton, J. H. C.

doi:10.1090/S0002-9939-1978-0515780-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An elementary proof of the classification of surfaces in the projective $3$-space
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by J. H. C. Creighton PDF

Proc. Amer. Math. Soc. 72 (1978), 191-192 Request permission

Abstract:

A closed surface embeds in the 3-dimensional real projective space if and only if it is orientable or of odd Euler characteristic. The proof given is elementary in the sense that only geometric techniques are used.

References

Glen E. Bredon and John W. Wood, Non-orientable surfaces in orientable $3$-manifolds, Invent. Math. 7 (1969), 83–110. MR 246312, DOI 10.1007/BF01389793

Hypersurfaces in lens spaces

E. Stiefel, Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten, Comment. Math. Helv. 8 (1935), no. 1, 305–353 (German). MR 1509530, DOI 10.1007/BF01199559