Vol.5, No 1, 2006 pp. 91 - 98
UDC 531.01
THE RECURRENT AND METRIC CONNECTION AND
F-STRUCTURES IN GAUGE SPACES OF THE SECOND
ORDER
Jovanka Nikić, Irena Čomić
Faculty of Technical Sciences, University of Novi Sad, Serbia
e-mail: nikic@uns.ns.ac.yu
e-mail: comirena@uns.ns.ac.yu
Abstract. Lately a big attention has been paid to the second order
gauge connection, but the investigations are mostly restricted to the d-connection.
Here this connection is generalized and a recurrent gauge connection is
given on the manifold E n+m+l .
Let us denote by TH(E),TV1(E),TV2(E) the subspaces
of T(E) spanned by adapted bases, then T(E) = TH(E) ? TV1(E)
? TV2(E) = TH(E) ? TV(E).
If an almost complex structure J on the tangent space T(E) of the gauge
E2n manifold and the fv (2k + 1,1) -structure on TV
(E) are given, then the fh (2k + 1,1) -structure on the horizontal
subspace is defined in the natural way. We can define the F(2k+1, 1)-structure
on T(E) using fv (2k + 1,1) and fh (2k + 1,1). The
condition for the reduction of the structural group of such manifolds is
given.
Key words: Generalized connection, gauge connection, f-structure
REKURENTNE I METRIČKE KONEKSIJE I F-STRUKTURE
U
METRIČKIM PROSTORIMA DRUGOG REDA
Skoro kompleksna struktura J je data na tangentnom prostoru mnogostrukosti
E dimenzije 2n i data je u vertikalnom tangentnom prostoru TV(E)
struktura fV(2k+1, 1). Tada se na prirodan način može dobiti
na horizontalnom prostoru TH(E) struktura istog tipa fH(2k+1,
1), pa i na celom tangentnom prostoru T(E) struktura f(2k+1, 1). Dobijen
je potreban i dovoljan uslov za redukciju strukturne grupe mnogostrukosti
da bi se ona mogla snabdeti f(2k+1, 1) – strukturom.U ovakvom prostoru
ispitivane su koneksije i izvršena je generalizacija d – koneksije.
Ključne reči: generalizovana koneksija, gauge koneksija,
f – struktura
