# Differential geometry of grassmannians and the Plücker map

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 873-884
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topSasha Anan’in, and Carlos Grossi. "Differential geometry of grassmannians and the Plücker map." Open Mathematics 10.3 (2012): 873-884. <http://eudml.org/doc/268939>.

@article{SashaAnan2012,

abstract = {Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.},

author = {Sasha Anan’in, Carlos Grossi},

journal = {Open Mathematics},

keywords = {Classic geometries; Plücker map; Hyperbolic geometry; classic geometries; hyperbolic geometry},

language = {eng},

number = {3},

pages = {873-884},

title = {Differential geometry of grassmannians and the Plücker map},

url = {http://eudml.org/doc/268939},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Sasha Anan’in

AU - Carlos Grossi

TI - Differential geometry of grassmannians and the Plücker map

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 873

EP - 884

AB - Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.

LA - eng

KW - Classic geometries; Plücker map; Hyperbolic geometry; classic geometries; hyperbolic geometry

UR - http://eudml.org/doc/268939

ER -

## References

top- [1] Anan’in S., Gonçalves E.C.B., Grossi C.H., Grassmannians and conformal structure on absolutes, preprint available at http://arxiv.org/abs/0907.4469
- [2] Anan’in S., Grossi C., Coordinate-free classic geometries, Mosc. Math. J., 2011, 11(4), 633–655 Zbl1256.53014
- [3] Borisenko A.A., Nikolaevskiı Yu.A., Grassmann manifolds and Grassmann image of submanifolds, Russian Math. Surveys, 1991, 46(2), 45–94 http://dx.doi.org/10.1070/RM1991v046n02ABEH002742 Zbl0742.53017
- [4] do Carmo M.P., Riemannian Geometry, Math. Theory Appl., Birkhäuser, Boston, 1992
- [5] Gromov M., Lawson H.B. Jr., Thurston W., Hyperbolic 4-manifolds and conformally flat 3-manifolds, Inst. Hautes Études Sci. Publ. Math., 1988, 68, 27–45 http://dx.doi.org/10.1007/BF02698540 Zbl0692.57012
- [6] Guilfoyle B., Klingenberg W., Proof of the Carathéodory conjecture by mean curvature flow in the space of oriented affine lines, preprint available at http://arxiv.org/abs/0808.0851 Zbl1060.51015
- [7] Kobayashi S., Nomizu K., Foundations of Differential Geometry. II, Interscience Tracts in Pure and Applied Mathematics, 15(2), John Wiley & Sons, New York-London-Sydney, 1969 Zbl0175.48504
- [8] Kuiper N.H., Hyperbolic 4-manifolds and tesselations, Inst. Hautes Études Sci. Publ. Math., 1988, 68, 47–76 http://dx.doi.org/10.1007/BF02698541 Zbl0692.57013
- [9] Luo F., Constructing conformally flat structures on some Seifert fibred 3-manifolds, Math. Ann., 1992, 294(3), 449–458 http://dx.doi.org/10.1007/BF01934334 Zbl0758.57009

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.