Rouse Co., developer of Columbia, Md., and retail shopping centers around the country, may begin managing 10 retail centers owned by the Aetna Life Insurance Co., Rouse President and Chief Executive Mathias J. DeVito told the company's stockholders today.

The company has reached an agreement in principle with Aetna to manage on an incentive fee basis the centers, which total more than 4.1 million square feet of retail space. Six of the centers are in Iowa, and one each is in Texas, Louisiana, Arkansas and Colorado, a Rouse Co. spokesman said.

"This increases from five to 15 the number of centers managed by our company on a shared-growth basis," DeVito said.

"The acquisition and management of centers developed or owned by others is an area of great opportunity for us, especially now at a time when institutional investors are acquiring a large number of centers from companies in our business who are liquidating or selling off a portion of their retail center holdings," DeVito continued. "This is a line of business that we will continue to pursue with vigor during the coming months."

DeVito added that despite inflation and recession, Rouse Co. should do well during the year. He said that "continued high short-term interest rates could have a temporary, but significant, impact on two retail projects scheduled to open later this year -- Harbor Place in Baltimore and Santa Monica Place in California -- since the interest rates on their construction loans are tied to the prime rate."

The interest charges on those projects will be reduced when permanent loans are settled later in the year, DeVito added. Harbor Place is scheduled to open July 2 and Santa Monica Place is expected to open three months later.

Rouse Co. already owns and operates 33 retail centers totalling 20 million square feet of retail space, DeVito said.

"Overall we are quite pleased with [the] results from our retail centers, especially in view of the unfavorable economic conditions that all of us in business have had to face in recent times," DeVito said.

"Most of the start-up losses from 1978 and 1979's new projects are behind us. And although the rate of merchant sales growth slowed down significantly during March and April, sales in our centers for the first four months of 1980 are about 7 percent ahead of 1979," he reported.