Orientable Surface

A Regular Surface $M\subset\Bbb{R}^n$ is called orientable if each Tangent Space $M_p$ has a Complex Structure $J_p:M_p\to M_p$ such that $p\to J_p$ is a continuous function.

See also Nonorientable Surface, Regular Surface

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 230, 1993.