Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
DEMONSTRATIO MATHEMATICAVol. XXXVINo 32003Wiestaw KrôlikowskiA CLIFFORD-TYPE STRUCTUREIntroductionIn the paper a Clifford-type structure is introduced and some considerations on Clifford-type manifolds are developped. First of all an analog of thefundamental 2-form of complex analysis is defined and using it a decomposition analogous to the Hodge Decomposition Theorem for Kahler manifoldsis given for Clifford-type manifolds. By the Chern Theorem [5] we get anincreasing sequence of Betti numbers for Clifford-type manifolds.1. A Clifford-type structureLet V be a real vector space.DEFINITION 1.1. An almost Clifford-type structure Cn on V is a set of nalmost complex structures { i i , . . . , /„} such thatIaIp+ Ipla= —26apld,a, (3 = 1,...,n,where Id stands for the identity endomorphism of V, 6 denotes the „Kronecker delta".REMARK 1.1. a) If n = 1, then Ci = {/} with I2 = -Id. Thus, C\ is nothingbut an almost complex structure. Recall that the standard form of an almostcomplex structure looks as follows:/ O =( - ° /O)'{ I =ID)provided that V has an even dimension (see, e.g. [10]).b) If n = 2, then C2 = {I, J} with I2 = J2 = -Id and IJ + JI = 0.Define K := I J, then IJK =
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 2003
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.