The measure of holomorphicness of a real submanifold of an almost Hermitian manifold
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- by Fernando Etayo PDF
- Proc. Amer. Math. Soc. 131 (2003), 2911-2920 Request permission
Abstract:
In this note we define the measure of holomorphicness $\mu (M)$ of a compact real submanifold $M$ of an almost Hermitian manifold $(\overline {M},\overline {J},\overline {g})$. The number $\mu (M)\in [0,1]$ verifies the following properties: $M$ is a complex submanifold iff $\mu (M)=1$; if $\dim M$ is odd, then $\mu (M)=0$. Explicit examples of surfaces in ${\mathbb C}^{2}$ are obtained, showing that $\mu (S^{2})=\frac {1}{5}$ and that $0\leq \mu (T)\leq \frac {3}{8}$, $T$ being the Clifford torus.References
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Additional Information
- Fernando Etayo
- Affiliation: Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s.n., E-39071 Santander, Spain
- Email: etayof@unican.es
- Received by editor(s): May 25, 2001
- Published electronically: April 9, 2003
- Additional Notes: The author’s research was partially supported by the Spanish Ministerio de Ciencia y Technología (BFM 2002-00141)
- Communicated by: Mohan Ramachandran
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2911-2920
- MSC (2000): Primary 53C40; Secondary 53C55
- DOI: https://doi.org/10.1090/S0002-9939-03-07112-0
- MathSciNet review: 1974349