Geodesic
On the Volume of the Trajectory Surfaces under the Homothetic Motions
Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 2 
M. Duldul; N. Kuruoglu. On the Volume of the Trajectory Surfaces under the Homothetic Motions. Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a12/
@article{AMUC_2007_76_2_a12,
     author = {M. Duldul and N. Kuruoglu},
     title = {On the {Volume} of the {Trajectory} {Surfaces} under the {Homothetic} {Motions}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2007},
     volume = {76},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a12/}
}
TY  - JOUR
AU  - M. Duldul
AU  - N. Kuruoglu
TI  - On the Volume of the Trajectory Surfaces under the Homothetic Motions
JO  - Acta mathematica Universitatis Comenianae
PY  - 2007
VL  - 76
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a12/
ID  - AMUC_2007_76_2_a12
ER  - 
%0 Journal Article
%A M. Duldul
%A N. Kuruoglu
%T On the Volume of the Trajectory Surfaces under the Homothetic Motions
%J Acta mathematica Universitatis Comenianae
%D 2007
%V 76
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a12/
%F AMUC_2007_76_2_a12

Voir la notice de l'article provenant de la source Comenius University

The volumes of the surfaces of 3-dimensional Euclidean Space which are traced by a fixed point as a trajectory surface during 3-parametric motions are given by H. R. Muller [3], [4], [5] and W. Blaschke [1]. In this paper, the volumes of the trajectory surfaces of fixed points under 3-parametric homothetic motions are computed. Also, using a certain pseudo-Euclidean metric we generalized the well-known classical Holditch Theorem, [2], to the trajectory surfaces.