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• W2015485423 abstract "A skew brane is a codimension 2 submanifold in affine space such that the tangent spaces at any two distinct points are not parallel. We show that if an oriented closed manifold has a nonzero Euler characteristic ({chi}), then it is not a skew brane; generically, the number of oppositely oriented pairs of parallel tangent spaces is not less than ({chi^2{/4}}). We give a version of this result for immersed surfaces in dimension 4. We construct examples of skew spheres of arbitrary odd dimensions, generalizing the construction of skew loops in 3-dimensional space due to Ghomi and Solomon (2002). We conclude with two conjectures that are theorems in 1-dimensional case." @default.
• W2015485423 created "2016-06-24" @default.
• W2015485423 creator A5053891463 @default.
• W2015485423 date "2010-07-23" @default.
• W2015485423 modified "2023-10-17" @default.
• W2015485423 title "Existence and nonexistence of skew branes" @default.
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• W2015485423 doi "https://doi.org/10.1007/s11784-010-0015-y" @default.
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