caa a22 4500 46324592X CHVBK 20180405153325.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s00009-007-0114-1 doi (NATIONALLICENCE)springer-10.1007/s00009-007-0114-1 Ghimenti Marco Dipartimento di Matematica, Università di Pisa, via Buonarroti 1C, 56127, Pisa, Italy aut Morse Theory for Geodesics in Conical Manifolds [Elektronische Daten] [Marco Ghimenti] Abstract.: The aim of this paper is to extend the Morse theory for geodesics to the conical manifolds. In a previous paper [15] we defined these manifolds as submanifolds of $${\mathbb{R}}^n$$ with a finite number of conical singularities. To formulate a good Morse theory we use an appropriate definition of geodesic, introduced in the cited work. The main theorem of this paper (see Theorem 3.6, section 3) proofs that, although the energy is nonsmooth, we can find a continuous retraction of its sublevels in absence of critical points. So, we can give a good definition of index for isolated critical values and for isolated critical points. We prove that Morse relations hold and, at last, we give a definition of multiplicity of geodesics which is geometrical meaningful. In section 5 we compare our theory with the weak slope approach existing in literature. Some examples are also provided. Birkhäuser Verlag Basel/Switzerland, 2007 Geodesics nationallicence Morse theory nationallicence nonsmooth analysis nationallicence nonsmooth manifolds nationallicence Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 229-244 1660-5446 4:2<229 2007 4 9 https://doi.org/10.1007/s00009-007-0114-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00009-007-0114-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ghimenti Marco Dipartimento di Matematica, Università di Pisa, via Buonarroti 1C, 56127, Pisa, Italy aut NATIONALLICENCE 773 0- Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 229-244 1660-5446 4:2<229 2007 4 9 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer