In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three obvious examples are Euclidean n-space, the n-dimensional sphere, and hyperbolic space, although a space form need not be simply connected.
Reduction to generalized crystallography
The Killing–Hopf theorem of Riemannian geometry states that the universal cover of an n-dimensional space form with curvature is isometric to , hyperbolic space, with curvature is isometric to , Euclidean n-space, and with curvature is isometric to , the n-dimensional sphere of points distance 1 from the origin in .
By rescaling the Riemannian metric on , we may create a space of constant curvature for any . Similarly, by rescaling the Riemannian metric on , we may create a space of constant curvature for any . Thus the universal cover of a space form with constant curvature is isometric to .
This reduces the problem of studying space form to studying discrete groups of isometries of which act properly discontinuously. Note that the fundamental group of , , will be isomorphic to . Groups acting in this manner on are called crystallographic groups. Groups acting in this manner on and are called Fuchsian groups and Kleinian groups, respectively.
Space form problem
The space form problem is a conjecture stating that any two compact aspherical Riemannian manifolds with isomorphic fundamental groups are homeomorphic.
The possible extensions are limited. One might wish to conjecture that the manifolds are isometric, but rescaling the Riemannian metric on a compact aspherical Riemannian manifold preserves the fundamental group and shows this to be false. One might also wish to conjecture that the manifolds are diffeomorphic, but John Milnor's exotic spheres are all homeomorphic and hence have isomorphic fundamental group, showing this to be false.
Modeling Systems in State-Space Form (Dr. Jake Abbott, University of Utah)
University of Utah ME EN 5210/6210 & CH EN 5203/6203 State-Space Control Systems The correct sequence to watch these tutorials can be found on the web page: ...
State Space Form from Bond Graph Models Part 2
This video will show you the fundamentals of generating equations in state space form and the automated generation of the A, B matrices using CAMPG.
Spaceform glass gifts
available from www.little-impressions.com - created at http://animoto.com.
ENB458: sampling time, aliasing and discrete-time state-space form
In this lecture we discuss the important topic of aliasing, how an infinite number of periodic signals look the same when sampled. We then move on to discuss...
Exhibition | Space Form Light: Architecture in Print
From the artistic constructs of historic artists Piranesi and Palladio to the present, this exhibition explores how architects do what painters do — but in i...
Joomla! RSForms - Add a "Reserve Your Space" Form
State Space Form from Bond Graph Models Part 1
This video will show you the fundamentals of generating equations in state space form and the automated generation of the A, B matrices using CAMP.
Angry Birds Crazy Adventures Episode 4:Meet The Birds Space Form
Space, Form, and Memory Project - Elements 2012
Space, Form, and Memory - Elements Project.
sample of "Architecture; Form Space and Order 3ed [CD]".flv
This video, I had captured while surfing a little through the CD, that comes with this excellent educational reference.
Tue, 11 Jun 2013 17:52:16 -0700
Time cease to exist without the form and space. Form, time and space exist together and disappear together. Past, present and future are within the waking experience. The past, present and future of the dream gets over when waking takes place. The past ...
Design & Trend
Design & Trend
Wed, 19 Jun 2013 10:57:07 -0700
Unlike flames on Earth, which expand, grow, and flicker, flames in space form spheres that wait for the Oxygen to latch onto it. Oxygen then combines on the surface rather than throughout the flame, resulting in a simpler process. Fire normally happens ...
Mon, 17 Jun 2013 15:37:39 -0700
No one has seen the innermost self or God by practicing religion or yoga or indulging in god glorification because it exists prior to the form, time and space. Form, time and space ceases to exist as reality when wisdom dawns. Nonduality does not need ...
Mon, 17 Jun 2013 11:39:53 -0700
Along the way, you will learn the elements of setting up a good composition, values, space, form and shape, as well as direction of lighting, shading, shadowing and blending that is needed to convey this element with balance and some color theory of ...
noho arts district
Thu, 13 Jun 2013 04:13:50 -0700
"The patrons and artists who regularly gather at Fringe Central Station, our social space, form the base of that group. But we don't stop there: We consider the entirety of the Hollywood neighborhood part of our community, and we strive to make it a ...
Wed, 22 May 2013 01:00:47 -0700
The two future strands of Empty Space form a direct sequel to Nova Swing. At the end of the second novel, Liv Hula sold her bar and bought a third share of a rocketship, along with two of her customers, Fat Antoyne and his girlfriend, Irene. Now the ...
Tue, 04 Jun 2013 04:27:35 -0700
A set designer should have an understanding of space, form and structure, composition, perspective, visual storyboard, design layout and lighting schemes. This goes for film, TV and even stage productions, some of which require very elaborate sets. It ...
Mon, 27 May 2013 07:11:52 -0700
As is, it's a bit rough, but the rough edges of the space form a fitting environment for Baxter's shabby career retrospective -- during renovations, it might make sense to stick to minimalist shows that can make the spray-painted walls work. "An ...
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