On the Existence of Almost Affinely Flat Structure Induced by Hypersurface Immersion on Connected Compact Manifold

Tagnon, Mèmègnon R.; Atindogbe, Cyriaque; Wali, Augustus N.

dc.contributor.author	Tagnon, Mèmègnon R.
dc.contributor.author	Atindogbe, Cyriaque
dc.contributor.author	Wali, Augustus N.
dc.date.accessioned	2018-10-01T06:53:55Z
dc.date.available	2018-10-01T06:53:55Z
dc.date.issued	2018
dc.identifier.citation	International Mathematical Forum, Vol. 13, 2018, no. 9, 427 - 435	en_US
dc.identifier.uri	http://www.m-hikari.com/imf/imf-2018/9-12-2018/p/tagnonIMF9-12-2018.pdf
dc.identifier.uri	http://repository.seku.ac.ke/handle/123456789/4266
dc.description	https://doi.org/10.12988/imf.2018.8842	en_US
dc.description.abstract	Given a hypersurface immersion and a transversal vector field, the formula of Gauss leads to an induced connection and a symmetric bilinear function called affine fundamental form. We define the norm of tensor field using the affine fundamental form (assumed to be nondegenerate) and prove that a hypersurface immersion on a connected compact 𝑛-dimensional differential manifold 𝑀 into the affine space ℝ𝑛+1 induces an almost affinely flat structure on 𝑀.	en_US
dc.language.iso	en	en_US
dc.publisher	Hikari	en_US
dc.subject	Affine (hypersurface) immersion	en_US
dc.subject	curvature tensor	en_US
dc.subject	almost affinely flat	en_US
dc.subject	Riemannian metric	en_US
dc.title	On the Existence of Almost Affinely Flat Structure Induced by Hypersurface Immersion on Connected Compact Manifold	en_US
dc.type	Article	en_US