Gauss map and List of Manchester United F.C. players: Difference between pages

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This is a list of [[Manchester United]] players with Wikipedia articles. This list includes not just the greats, but also the near greats.

In [[mathematics]], the '''Gauss map''' for a surface <math>S</math> lying in 3-space, associates to any point <math>p</math> of <math>S</math> the unit (normal) vector <math>N=N(p)</math> that is orthogonal to the tangent plane to <math>S</math> at <math>p</math>. Hence <math>N</math> is a map from <math>S</math> to the unit sphere <math>S^2</math>.

=='''A'''==

There arises the question of choosing the normal vector <math>N(p)</math> among the two possible choices (namely <math>N</math> and <math>-N</math>). Moreover we will require the Gauss map to be continuous: no jumps are allowed. There is no a priori "better" choice, however the ability to choose a (continuous) Gauss map is equivalent to the surface being [[orientable]]. However it is always locally true (i.e. on a small piece of the surface).

*[[Arthur Albiston]]

*[[John Anderson (footballer)|John Anderson]]

*[[Viv Anderson]]

*[[John Aston Sr.|John Aston (father)]]

*[[John Aston|John Aston (son)]]

=='''B'''==

The notion of Gauss map can be generalized to a submanifold <math>S</math> of dimension <math>k</math> in an ambient manifold <math>M</math> of dimension <math>n</math>. In that case, the unit normal vector is replaced by the tangent <math>k</math>-plane at the point <math>p \in S</math>. (It should be noted that in euclidean 3-space, a 2-plane is characterized by its unit normal vector -- up to sign, hence the definition above.) The Gauss map then goes from <math>S</math> to the set of tangent <math>k</math>-planes in the tangent bundle <math>TM</math>. The situation is somewhat simpler in euclidean <math>n</math>-space, where the target set is the [[Grassmannian]] <math>G_{k,n}</math>: the set of all (oriented) <math>k</math>-planes in <math>\mathbb{R}^n</math>. (In the introductory example, <math>G_{2,3} \simeq G_{1,3} \simeq S^2</math>.) In a more general manifold <math>M</math>, the target space for the Gauss map <math>N</math> is a Grassmann bundle built on the tangent bundle <math>TM</math>. The question of the (global) existence of <math>N</math> is then a non trivial topological question.

*[[Gary Bailey]]

*[[Jimmy Bannister]]

*[[Fabien Barthez]]

*[[David Beckham]]

*[[David Bellion]]

*[[Geoff Bent]]

*[[Henning Berg]]

*[[Johnny Berry]]

*[[George Best]]

*[[Clayton Blackmore]]

*[[Laurent Blanc]]

*[[Jackie Blanchflower]]

*[[Jesper Blomqvist]]

*[[Mark Bosnich]]

*[[Shay Brennan]]

*[[Wes Brown]]

*[[Steve Bruce]]

*[[Martin Buchan]]

*[[Herbert Burgess]]

*[[Nicky Butt]]

*[[Roger Byrne]]

=='''C'''==

*[[Eric Cantona]]

*[[Noel Cantwell]]

*[[Johnny Carey]]

*[[Roy Carroll]]

*[[Joseph Cassidy]]

*[[Luke Chadwick]]

*[[Bobby Charlton]]

*[[Allenby Chilton]]

*[[Henry Cockburn_(footballer)|Henry Cockburn]]

*[[Andrew Cole]]

*[[Eddie Colman]]

*[[John Connelly]]

*[[Steve Coppell]]

*[[Pat Crerand]]

*[[Jack Crompton]]

*[[Jordi Cruyff]]

=='''D'''==

*[[Gerry Daly]]

*[[Peter Davenport (footballer)|Peter Davenport]]

*[[Jimmy Davis (footballer)|Jimmy Davis]]

*[[Jimmy Delaney]]

*[[Eric_Djemba-Djemba]]

*[[Mal Donaghy]]

*[[Robert Donaldson]]

*[[John Downie]]

*[[Dick Duckworth]]

*[[Tony Dunne]]

*[[Michael Duxbury]]

=='''E'''==

*[[Duncan Edwards]]

=='''F'''==

*[[Rio Ferdinand]]

*[[John Fitzpatrick]]

*[[Darren Fletcher]]

*[[Diego Forlán]]

*[[Alex Fortsyth]]

*[[Quinton Fortune]]

*[[Bill Foulkes]]

=='''G'''==

*[[David Gaskell]]

*[[John Gidman]]

*[[Ryan Giggs]]

*[[Andy Goram]]

*[[Brian Greenhoff]]

*[[Jimmy Greenhoff]]

*[[Harry Gregg]]

=='''H'''==

*[[Gabriel Heinze|Gabriel Iv&aacute;n Heinze]]

*[[David Herd_(footballer)|David Herd]]

*[[Lal Hilditch]]

*[[Tim Howard]]

*[[Mark Hughes]]

=='''I'''==

*[[Paul Ince]]

*[[Denis Irwin]]

=='''J'''==

*[[Ronny Johnsen]]

*[[Mark Jones]]

*[[Joe Jordan]]

=='''K'''==

*[[Andrei Kanchelskis]]

*[[Roy Keane]]

*[[Brian Kidd]]

*[[Kleberson|José Kl&eacute;berson Pereira]]

=='''L'''==

*[[Denis Law]]

*[[Jim Leighton]]

=='''M'''==

*[[Lou Macari]]

*[[Lee Martin]]

*[[David May]]

*[[Brian McClair]]

*[[Sammy McIlroy]]

*[[Paul McGrath]]

*[[Gordon McQueen]]

*[[Billy Meredith]]

*[[Liam Miller]]

*[[Charlie Mitten]]

*[[Remi Moses]]

=='''N'''==

*[[Gary Neville]]

*[[Philip Neville]]

=='''O'''==

*[[John O'Shea]]

=='''P'''==

*[[Gary Pallister]]

*[[Paul Parker]]

*[[Stan Pearson]]

*[[Stuart Pearson]]

*[[David Pegg]]

*[[Mike Phelan]]

*[[Karel Poborsky]]

=='''Q'''==

*[[Albert Quixall]]

=='''R'''==

*[[Ricardo Lopez Felipe]]

*[[Kieran Richardson]]

*[[Mark Robins]]

*[[Bryan Robson]]

*[[Cristiano Ronaldo]]

*[[Wayne Rooney]]

*[[Jack Rowley]]

=='''S'''==

*[[Louis Saha]]

*[[Albert Scanlon]]

*[[Peter Schmeichel]]

*[[Paul Scholes]]

*[[Les Sealey]]

*[[Lee Sharpe]]

*[[Mika&euml;l Silvestre]]

*[[Alan Smith]]

*[[Ole Gunnar Solskjær]]

*[[Jonathan Spector]]

*[[Joe Spence]]

*[[Harry Stafford_(football)|Harry Stafford]]

*[[Jaap Stam]]

*[[Frank Stapleton]]

*[[Alex Stepney]]

*[[Nobby Stiles]]

*[[Gordon Strachan]]

=='''T'''==

*[[Tommy Taylor]]

*[[Sandy Turnbull]]

=='''U'''==

=='''V'''==

*[[Ruud van Nistelrooy]]

*[[Juan Sebastián Verón]]

*[[Dennis Viollet]]

=='''W'''==

*[[Neil Webb]]

*[[Liam Whelan]]

*[[Norman Whiteside]]

*[[Ray Wilkins]]

*[[Walter Winterbottom]]

=='''X'''==

=='''Y'''==

*[[Dwight Yorke]]

=='''Z'''==

[[Category:Manchester United|List of Manchester United Players]]