Real projective space as a space of planar polygons [PDF]
arXiv, 2015 We prove that real projective space RP^{n-3} is homeomorphic to the space of all isometry classes of n-gons in the plane with one side of length n-2 and all other sides of length 1. This makes the topological complexity of real projective space more relevant to robotics.
arxiv +3 more sources
Spaces of algebraic maps from real projective spaces into complex projective spaces [PDF]
arXiv, 2008 We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural "degree" filtration approximate ...
Kozlowski, Andrzej, Yamaguchi, Kohhei
arxiv +3 more sources
Lagrangian Floer homology of the Clifford torus and real projective space in odd dimensions [PDF]
, 2009 and real projective space is RP k = { [z0 : · · · : zk] ∈ CP k | zi ∈ R }. They intersect in the 2 points [±1 : · · · : ±1]. Two interesting questions to ask are the following: Can they be disjoined from each other by Hamiltonian isotopy? If not, what is
Garrett Alston
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Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie 𝔻-parallel [PDF]
Canadian mathematical bulletin, 2011 We prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\mathbb{D}$ -parallel and satisfies a further condition.
Juan de Dios Pérez, Young Jin Suh
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The homotopy of spaces of maps between real projective spaces [PDF]
Journal of the Mathematical Society of Japan, 2006 We study the homotopy groups of spaces of continuous maps between real projective spaces and we generalize the results given in [5], [8] and [12]. In particular, we determine the rational homotopy types of these spaces and compute their fundamental groups explicitly.
Kohhei Yamaguchi
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On the immersion problem for real projective spaces [PDF]
Bulletin of the American Mathematical Society, 1963 I. M. James
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Approximating submanifolds of real projective space by varieties
, 1976 Henry C. King
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Compact minimal hypersurfaces with index one in the real projective space
, 2000 Manfredo do Carmo +2 more
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Compactness of the Automorphism Group of a Topological Parallelism on Real Projective 3-Space [PDF]
Results in Mathematics, 2017 We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.
D. Betten, R. Löwen
semanticscholar +2 more sources
Packings in Real Projective Spaces [PDF]
SIAM Journal on Applied Algebra and Geometry, 2018 31 pages, 2 ...
Matthew Fickus +2 more
openaire +3 more sources