Acerca de la Geometría de Lobachevski by A. S. Smogorzhevski

By A. S. Smogorzhevski

Show description

Read or Download Acerca de la Geometría de Lobachevski PDF

Best geometry and topology books

Convex Optimization and Euclidean Distance Geometry

Convex research is the calculus of inequalities whereas Convex Optimization is its program. research is inherently the area of the mathematician whereas Optimization belongs to the engineer. In layman's phrases, the mathematical technological know-how of Optimization is the research of the way to make a good selection while faced with conflicting necessities.

Extra resources for Acerca de la Geometría de Lobachevski

Example text

3. 2 Pseudo-Hermitian symmetric spaces. We have seen in the previous section that in order to classify indecomposable pseudo-Hermitian symmetric spaces one would have to classify the objects (O1)–(O3) for ˆl being a complex grading. This task is of a similar complexity as the classification of all symmetric spaces discussed in Section 3. 1/-equivariance and making some aspects of the theory simpler then for general symmetric spaces. 3, Table 1) admit a Kähler structure. The classification problem for pseudo-Riemannian symmetric spaces 33 We treat pseudo-Hermitian symmetric spaces together with para-Hermitian ones because of the similarity of their behaviour.

L / Š R and D . L/ej0 (7) (8) 26 I. Kath and M. Olbrich for L 2 l, i D 1; : : : ; p and j D 1; : : : ; q. l; Âl ; a WD . R; id/-module for which the 1-eigenspace of the involution is positive definite is of the kind defined above. 0; 0/g and indecomposability Since l is one-dimensional we have HQ and admissibility conditions are easy to handle. 2 (Cahen–Wallach [17]). p; q; ; /, p; q 0, p C q > 0, . ; / 2 Mp;q , where ˇ 0< 1Ä Ä p; 0 < 1 Ä ˇ Mp;q WD . ; / 2 Rp ˚ Rq ˇ 1 D 1 if p > 0; 1 D 1 else Ä q ; : Cahen and Wallach [17] constructed explicit models for all simply connected Lorentzian symmetric spaces.

4. are C; C; S 2 Š CP 1 , and H 2 , respectively. The complex gradings of l correspond to the natural complex structures of these spaces. Note that the data defined in 4. do not depend on the choice of the square root of z. l; ˆl /-modules in cases 3. and 4. 3. 1 differs slightly from the corresponding statement in [36]. 2; 2q/ that admit the structure of a pseudo-Hermitian symmetric triple, whereas here we have determined isomorphism classes of pseudo-Hermitian symmetric triples. Comparing both results we find that all of these symmetric triples admit exactly one complex grading (up to isomorphism).

Download PDF sample

Rated 4.18 of 5 – based on 47 votes