Particular trace decompositions and applications of trace decomposition to almost projective invariants

Mircea Crâşmăreanu

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 3, page 631-637
  • ISSN: 0862-7959

Abstract

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First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors.

How to cite

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Crâşmăreanu, Mircea. "Particular trace decompositions and applications of trace decomposition to almost projective invariants." Mathematica Bohemica 126.3 (2001): 631-637. <http://eudml.org/doc/248865>.

@article{Crâşmăreanu2001,
abstract = {First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors.},
author = {Crâşmăreanu, Mircea},
journal = {Mathematica Bohemica},
keywords = {traceless tensor; trace decomposition; almost projective invariant; traceless tensor; trace decomposition; almost projective invariant; Weyl curvature tensors},
language = {eng},
number = {3},
pages = {631-637},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Particular trace decompositions and applications of trace decomposition to almost projective invariants},
url = {http://eudml.org/doc/248865},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Crâşmăreanu, Mircea
TI - Particular trace decompositions and applications of trace decomposition to almost projective invariants
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 3
SP - 631
EP - 637
AB - First, by using the formulae of Krupka, the trace decomposition for some particular classes of tensors of types (1, 2) and (1, 3) is obtained. Second, it is proved that the traceless part of a tensor is an almost projective invariant of weight 1. We apply this result to Weyl curvature tensors.
LA - eng
KW - traceless tensor; trace decomposition; almost projective invariant; traceless tensor; trace decomposition; almost projective invariant; Weyl curvature tensors
UR - http://eudml.org/doc/248865
ER -

References

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  1. Almost projective invariants for a (M, A)-manifold, Proceedings of Romanian Conference of Geometry and Topology, Târgovişte, 1986, Univ. Bucureşti, 1988. (Romanian) MR0979993
  2. The trace decomposition of tensors of type (1, 2) and (1, 3), New Developments in Differential Geometry (Debrecen, 1994), Math. Appl., 350, Kluwer Academic Publ., Dordrecht, 1996, 243–253. Zbl0840.15024MR1377288
  3. The trace decomposition problem, Beiträge Algebra Geom. 36 (1995), 303–315. (1995) Zbl0839.15024MR1358429
  4. On the general trace decomposition problem, Proc. Conf., Aug. 28–Sept. 1, 1995 Brno, Czech Republic, Masaryk Univ., Brno, 1996, pp. 45–50. (1996) MR1406322
  5. On the special trace decomposition problem on quaternion structure, Proceedings of the Third International Workshop on Differential Geometry and Its Applications and the First German-Romanian Seminar on Geometry (Sibiu, 1997), Gen. Math. 5 (1997), 225–230. (1997) MR1723612
  6. Leçons de Géométrie Différentielle, vol. I, Ed. Academiei, Bucarest, 1957. (1957) MR0124823
  7. Leçons de Géométrie Différentielle, vol. III, Ed. Academiei, Bucarest and Gauthier-Villars, Paris, 1964. (1964) MR0124823

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