Generic immersions and totally real embeddings-Reference-Cited by-同舟云学术

Generic immersions and totally real embeddings

Published:2018-10 Issue:11 Volume:29 Page:1850073
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Kasuya Naohiko¹^ORCID,Takase Masamichi²

Affiliation:

1. Department of Mathematics, Kyoto Sangyo University, Kamigamo-Motoyama, Kita-ku, Kyoto 603-8555, Japan

2. Faculty of Science and Technology, Seikei University, 3-3-1 Kichijoji-kitamachi, Musashino, Tokyo 180-8633, Japan

Abstract

We show that, for a closed orientable [Formula: see text]-manifold, with [Formula: see text] not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex [Formula: see text]-space ensures the existence of a totally real embedding into complex [Formula: see text]-space. This implies that a closed orientable [Formula: see text]-manifold with non-vanishing Kervaire semi-characteristic possesses no CR-regular embedding into complex [Formula: see text]-space. We also pay special attention to the cases of CR-regular embeddings of spheres and of simply-connected 5-manifolds.

Funder

Japan Society for the Promotion of Science

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X18500738

Reference34 articles.

1. Vector Fields on Spheres

2. Vector Fields on Manifolds

3. Vector fields with finite singularities

4. Fibrés normaux d’immersions en dimension double, points doubles d’immersions lagrangiennes et plongements totalement réels

5. Simply Connected Five-Manifolds

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. CR regular embeddings of ⁴ⁿ⁻¹ in ℂ²ⁿ⁺¹;Proceedings of the American Mathematical Society;2020-03-17

2. Erratum: Generic immersions and totally real embeddings;International Journal of Mathematics;2019-11